{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 可视化三维样本数据点的PCA过程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from mpl_toolkits import mplot3d\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 在三维空间随机生成100个样本点\n",
    "np.random.seed(8888)\n",
    "X_random = np.random.random(size=(100, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SovfuKsET3WEsFgu9vb0aAdQGmJdD2K7izTuq+ebTA4zNBRFAfbGZvc1lWAw6qqqqALSE3dDQEF6vF5vNpmXoLRbLy24Fz3ZsSZLYvHkzZrOZ++67b7lPWwcMJ/x55NTfvbwJnqm2DXHzhL6+Pmw2G6tWrVrUcbMRPBQK0dbWRmFhIbt37076MZcSbkuSRCQS4fDhw9hsNnbs2KHdJCoBwuEwBw8exG63a2Wc801imkrGlgob//eqNXQ7fJj0OlrrCjCndLWpK5zaOKLqyLu6ugiFQlgsFkKhEOFweFl74FeS4JB93NQKbcfSnTDric5rgmcbE5Q4cGDXrl20tbUt+viZ6uBOp5OOjo60pTX1fYtdwVV57Lp166iqqtKSg3CaAKOjo+zevRuv14vT6dQkpme7Jzzbipru36oLzVQXZh6UkIhUHbmiKExOTjI8PEx7e/uy9sCvJMGzETgaja7U7zQCNCT8uR4Yy/Ba4DwmeDYrpdSBA7FYbFkUaeo8L1XemK0raTFP6JGREWZnZ9m4caMWtmYiUGLGetWqVUk94f39/VqCq7S0lMLCwmUNbcfngjzS5sDpC7Oq1ML1W6soNK/sLSLLMna7nYKCAjZu3KipzJxOZ9oe+MUQdqVX8Ezw+XzYbLaVOPQjwF2SJN1PPLk2l23/DecpwTN5kgshGBoamjdw4Exln3Ba7Wa32xc0V8z1fKpFk6IoVFZWZh0HlAmpPeHhcBin08nY2BgnT57EYrFoFk+Z+qJzgS8U5f5DY+h1MjVFJkZng/ziyDi3X5TcQrsS++VEIqaT1Kpdfz09PRgMhiQvt2zXspIEz3ZeNc+whGPeB1wBlEuSNAL8C2AAEEJ8B3iceImsh3iZ7B0LHfO8Inhq906q3PT48eOYTKZ5AwfO9IZT/c7Xrl2r1TqzIZcVXO0Hr62tjVs0dXYuy77MaDQmKc78fj9Op1NrES0sLNQIvxg4/RHCUUXrT68sNDE2FyQQUbAakwcXrIRUNdMxE3vgIXlEssfj0Samqgm7xOOsZHY+G5aqYhNC3LrAvwvgg4s55nlDcCEEU1NT2kTMxB9KJWBLS4sW4i7XOUOhEF1dXezcuTNnCeZCK7jqxprYD74SdfBEIwR1P+t2u3E6nQwPDxMKhbDZbJjN5gXDW7NeRhGgKAJZlghFFQyyhFEff48/HON/XxrjYNcstWUKb7/ESEPJ8khW1eRpLkgdkaw6vfT29hIIBDRJbWlp6TlTyK1giL5onBcEV0Py8fFxysrKNKKlDhxYTg10JBKhra0NIcSi/c4zkVVVus3Nzc2rxZ8NoYssy1oLJMDAwACRSISpqSktvFXD31Qjw4oCExetLuZAvwtZlhAC9rdWoT/VpfY/B4ZpH/eilyUc3jDf/OMAn7qmZVksopbqEpPO6cXj8WgJSr/fj9VqxWAwnFEPfCrS6dAT4fV6zwuZKpxjgqcm0vR6vbYyqsqx5R44AHGRSXt7Oy0tLQSDwUUfOx1Zw+Gwdr3p3FhzJfhyhsA6nQ6z2aw5lwaDQS15pYaRieW4164vZ22lDX84RqnVQEVBvEQXiSm0j3mpLjQyO+vHZjHgCsYYdgWXjeDL8ZkTjR9Wr15NX18fEE/Kqm2hiQm7pc6VW4jg+RWc9FZKOp2OWCy2YgMH1CTd+Pg4O3bswGq10tvbu+jjpIbo6gMj2x4+F4Krr8l2s8eU+DEy9X9ne7/ZbKa2tlarR6vluI6ODiKRCEVFRZSWllJTllye0skSep1EJCbiRVchiClg0i/PQ3cxIfpiUVhYqHWJqW2hqT3wasIu1wf9Qhr386WTDM4RwTONCZJlmbGxeFlvKQMHst3ckUiE9vZ2TCYTe/bsmTfxcjE3mKpkE0IwPDzM2NiY9sDI9p5sBI8pgi5njMnjDioLzWyvL8SgS+41Pjbq4dhofNTRpho7OxqK4v3gwFwgwgOHx+mb8lNiM/A3O2shy/nSleMSy1OqSYJqAPHWnTX87IVRPP4YHiXMrlWlNJdn/ryLwUoZOabuwVPbQlOHL+Tixa4ed6EV/BVJ8Gy1bb/fz+DgIHa7nR07diz6iZ7NCFGtmzc1NVFTU5P0b7msmunOFQqFOHLsGA6/oL5xIzE5uwJrIYL/5riD5ydiNMpejox6GHIGuGl7tXZdfdN+Dg/PUVVoQpKgbdSD3aRnfZUdIQQ/e2GM0dkAVYUmvKEYP3humJvXGyjNURiWWp4Kh8NJN3+h2czbttjpGg2ydnUNF6+tWtBFJlespFQ1GxEz9cAnbmFUwifmf3IJ0dWHyLnGWSN4NrmpOnCgtrZ2yb5W6QiurrCjo6Ns27Yt7b5Ifd9iVpBwOMzA4BDt4TJG/Tp0EyOYDTLvubyJmqLFi2PcwShtYx4qLBJlNiNIEl0OHzO+COX2OEMn3SGsRp1GKrtZz6Q7xPoqO8GowrArQHVh3CKo0Kxnwh1k2hejdIkLidFopKqqiqqqKu3mdzqdiNkQetcA3SddyzZiaaWy3YtpF83WA69KatUSZC4EX6xseqWw4gTPZqWUOnDA5XIxNze3pPOo+3c1UxqNRjl+/Dg6nW5e3TwRixXJTE5OMjg4iMdQzLBTpqEkXtJz+sL84sgYH3h1c9r3ZSO4+veSFI+qZXm+DVOhRU9w+vR1BiMx7Kb4ZzLqZAx6mVBUwWzQoQhBTIDFsDyrYuLNPzs7S1NTE9FoVBuxpCgKxcXFlJaWLil5dT42myRuYRobG7USpMvlYnJyUvNiUz9zYs5iib3gVxPv9dYB/y2E+HLKvxcBPwEaifP2X4UQ9y503BUleDYrJa/XS1tbW9LAAZWkS0EiUT0eD21tbaxevTpp7thC78uGRP+1tWvX8kzPNDr5tMjGbtLj9EUyvj+V4InfRaFZz9oKK3+dAnswgj8iaCwxU2I9naFeV2ln2BVkwh0fwVNmM7CpJm73rJMl3ry9mvtfHAMiCAGXNBdTaQst+LkWC3W/nDhiKV3ySg3307WHZjpmKuYCp8U3S9kOLGdkkFiCNBqNxGIxbDYbTqeT/v5+LWcRjUYXXSaTJEkHfAt4A3G9+QuSJD0ihDiR8LIPAieEEG+UJKkCOClJ0k+FEOFsx14xgmeTm46OjjI0NMTWrVuTPMnPhODqe0dGRhgeHk6SsmZDLgRXS3alpaXs3LmT6elpKm06xLQgFFUw6iQc3hB7V2dWjyUSPBaLcfz4cTwej5bIum5zBd6pEYx2IzXFVvY1FSfd1Ea9zBs2VuD0hRECSm2GpCRca10hlQUmpjwhbCY9TWUWhoeH513HmSLdapuavFLVZontoSrh08l1FUVJWgGFENx/aIzfHJ9CkqCxxML/eX3zoktyKyl0MRgM8yTEs7OzfO973+Oxxx6jvb2dm266iTvuuCOXStBeoEcI0QdwSmu+H0gkuAAKTrm62AEnEF3owMtO8Gx922pHlV6v56KLLpoXyp0JwQG6urowGo3s2bMn526ehQiuqujWr1+v3cCyLFNukbluczm/63QQVWBrbSHXbanOeByV4H6/n6NHj1JXV0dzczNut5vp6Wlme3pYYw1RXxGlstKctgSllyUqCzJXFqoLTVQXrnx76UIrcqraTN3LdnZ2Eg6HtW6xkpISzWI48ZgvDbt5rN1Bud2ILMGA088PD4zw4dc0Leo6V3Jvn1rhUW2dPvnJT9LV1cUHPvABhoaGct3+pevzTnVquYd4s8kYUAD8jRBiwYMvK8GFEExPTxMMBqmoqEj60RIHDqRmslUsleBer5fp6Wnq6+tZt27dot6bieBCCAYHB5mcnJynonthyMP3n5vCZPZRW2zmI69dQ21xdpWdJEl4PB6GhobYvHkzhYWFhMPhpJXvpZdeQqfTaU6malKntLQ0JxXWsCvAiCuA1ahjXdXKlGmyVQIUIRh0BghHFWqKzBSa9fP2some5IODg1p0lygtHXYFgNO1/iKLgd5p/6KvdSUJvlCSbcOGDbz+9a/P9ZC59HlfBRwBXgusAX4nSdJfhBDubAdeNoKrum6/34/H49EEH0LMHziQCUvpChsdHWVwcJCKiooliWLS9YRHo1Ha29u1aCDxJhl2BfjhixNY9DIVhSYm5kL855/6+cL+zP7X6oPP4/Fw0UUXYTKZ0n5OnS7ugqImdVTZ5cjICEIIjezpfM66HF7+1DWDxagjHFPonvKzvVhh+ewTTn+WdCt4TBH8/NAYx8c9yLKEWS/zzn0N86oK6brFOjs7mZ2dxeFwYDab0YXMxGKKpov3BqNsrl3ceCk4d9l5v9+/2HFYufR5vwP48qmGkx5JkvqBDcDBbAdeNoKrT2KDwaCtwpkGDmS8GL0+5xVcbcWMxWLs3buX/v7+Ja3+qfZLXq+XY8eOzUvQtY+5aRudw+GJ74ENpz5Kud1A37SfaExBr5v/+dSHRTQapaGhIat4J3GfnprIUtsmJyYmtDbRsrIyrYvq8LCbcrsR0yk3lfHZIFOGGPZFyvf94RiTnhB6WaK2yDwvuZWJ4J2TXtrGPDQUx6sKLn+EXx2b5H2XZy8XGQwGrFarloUPBAIUTc9waGiWoxNODHod5QVmbtu5tCajlcjO57KCZ1vI0uAFYK0kSU3AKHALcFvKa4aA1wF/kSSpClgP9C104GUN0WVZ1kiabeBAtvfnQlKfz8exY8eSMvDq6j/lCfHgS6M4fRF2NhZz1abKeNkpDYQQhBW0c46Pj9Pf3z8v+ffkCQdfebKbqCKIKQrBSIxNZfEf2BeKUWI1pCW3ep2NjY1IkqQNoV8KEtsmE9tE1Rrt+JSesiI7+sKC+M0nZRWypYXTF+ZnL47hC0VRBKypsHLT9hqt4SQb/OEYsnSaUDajjll/5qpCItSVVi3HrWq08i8N9Qy7ArjmPJiiXiYHuhjvO7Ny3HJhIQFNatJwIQghopIk3QX8lniZ7AdCiOOSJL3v1L9/B/g88ENJktqIh/QfE0JML3TsZU+yybKMy+XC7/dndUXJ9N6F9NoqCbds2UJh4WmDfZ1OhzsQ4au/P8GsP4JRJ3FoaBanP8zb9jbMO87EXJDPP36S7vFZbGYXt24aZm0R7NmzZ95+95t/7MWklynQywhFMDYXZNQdRRjC6HUS//D6+bVvVU+/ZcsWioqKNAluNuTakJKuTTTaNc6fuhyMO2aICii027AXGxfVwfaHrhlt/wzQNenj5KSXzTWnH3aZVnBVZBOKxiW8PVM+ttYVoAihyWkzId0xJUmisdRKY6kViK/eZ1qOWy5kW8GXWtMXQjxO3NAh8e++k/D/x4ArF3vcZSV4IBDQLIWzDRxYClJFMalPSFmWOT7qw+WLUFEQ33lajQqPtk1w2575riSff/wkI7MBikwS/mCQHx6N8d9vn09uRRH4wzEKTlkXSbJEgUnH61aZuO7iFuqLLZpJgnrs3t5eXC5XUstopoeXLxRFliUsBt2SW0plWWbf+lrKS4sYmAlglAX15gguxxh9rhlmZma0cD7bFsHlj2Aznb5xjXoZTzC5EpPpBm4osfCWHTXc9+IoR0bcWI06YkLwvb8OcecljVnr2LmSIp2W3Ol0zivHpUpL033Ox9onmfSEWVNu5epNFfOMIrNhoRAdVmZrsBQsK8HHxsZobm7WsqPLBdUdpaamRgt3UxEnkJKUj8xElUBEYcjpp9Ao4fWFsVvMhNEz6AzMy4bLssQlzaU82+fEdiqBpdNJ7Kwy0FpXlPTaaDTKsWPHsNls7Nq1a17OIZG84ajCg4fH6Z6KZ4cvbiqh8gz6xSVJYl2lnXWVp7PnQ1Jc2We32+eZOJaWllJcXJx0o64pt3JgYJa6IpmoIojGlEWV3bbXF/LECQcbq+2U2eLRw+FhN8dG3exoKMr4vqUmw0wmU1I5zufzJW1bQqEQU1NTWjkO4grAb/9lkFl/BLtZz597nLj8Ee64uD7ne3ahJNtK9/0vBstK8JaWFiKRyJJaMDNB1amroW4m6HQ61pYaKbUamPKEMOplghGFm3fVzfvhTDoJSYky54tgM5mRZBklRpJyLBEfv3od//77Hl4cnKWq0Mxdlzeimx1Keo2anMtUBkxdwf/cPUOXw0dtkRlFwDO9TnYWxmheCdcXu52ozkxNXQM6STA7O4vT6aSvry/JBOLS5hK8oSgdE150ssSVmypYXZacLFpotZ3xhU9HO5KEJMW19tmwHFJVSTrt1qpWIZ5//nncbre24JSUlODGyow3TG1xfBtiNci0j3nmWVNlQ7YH0nJbP58pVmQPfqZPMCHiAwJOnjxJ25iHmL2B8ESYVxeIjAkzWZax6OFLN27m4SNjzPjC7Goo5vUbkxN8atvo322187OOEN5IBEXEeOP2atZnqB3bTXr++boN2p9DoRBtrtOfcXJykt7e3nnJuXSfS8Wg00+RxRCX6Epg0ctMB87MODLd+V4a9fPdXx3CHYwiS/CR1zZx/ZYqraSYagLRUlDArq2llJWWYE4Tzi9Exg1Vdl4aclNVaCQSi3/e+uLseZiV6gfX6/WsWbMGOG3eODjowOmcRRfSYbVYMZji3XmLkcKmyq4TcT6ZPcAyE3y5XDn8fj9tbW28NGfhgeNhYmIQnSSxr9nBF27YlJbkaga+zG7k3ZetTntsVaPe1NTEjh01XLYjyIudg9iNEldsb8r5+tWMvRCC7u5uPB5P2uRc6udKJHhlgYmxWT92U1zJFYoJiu1n/nBUIYTgf9vneOD4HJFY/AYusuj5+h/6WV9pZ21l/CZMNYFQPd2Ot49qDihq1jqXMPqWXbX4wwodEx70OonbdteypiL7Db8S/eCpx1SrEGXlFXSHhmgbnSMQiOBz+tleLujt6tQimTNZgZfqqLpSOC882RIRi8U4fPgw6zZs4hM/OoHZIKOX4+Q40O+ifcxNa/38UD1xAGE6jI2NMTAwkKRRrykys6uhgFAohCIgEI5iM+oWJLokScRiMV566SUKCwuXNB/8NevLGZ7xaSN/NlTZaTFFlo3g7WMe/jroIxIT8e8P8ASjFJr19E77NIKnXmNq7T1xbK7ZbCYcDhMIBDLWeW0mPR+6YjWhqIJelnJaGVeimyxTGK2TJd6xr4EXBguY8UVoLDGztbZAc7dJHL6QLk+hXm8mnE9mD3AeEVxRFLq6ugiHw+zZswdFb0Yg0J363eOhrIQ3lH4/l0kFpyiKpoFOl32XJIlj436+8JfDhKIKdcUW/vH1LVRlSS75fD48Hg/btm3L2eU1leB2k5479tUz7YsgSxKVBUZOds7mdKxc4PRHkGUJgyyhCJBliMbi30+FPbfEWeKcbLUn/PDhw5pFs2rxlJjEUrEYO6eVUJxlq1UbdDKXNCdPnk30clOHTah5CtXaSXW3yYZXRIiuqsNy/dECgQDHjh2joqJCm7ZpN+tpLrfRO+3DZtDFu7b0Muur0n/B6XTs6nGrqqrYuHFj2lVi2h/jJ0dcVJQUUGw1MuEO8vU/9PClGzenPY9ah7dYLIuycE7XLmrQydQmSDmXWiZLB9XSuLHIyOBchGhMoJNl3rChgp0NhQu8ez5UEYrRaKS1tRVFUTSLJzWJVVpaSllZ2YIDCVKxEiv4mcwGTx02oVo7qV7soVCI0dFRTUWYiJXoBT/1miuArxMfhDAthHh1LsdekRVcVbPl8gWrgpBNmzZRUlJCW1ub1j/+1Zu28PnHT3J83E1NkZlPXrOeMnv6/VHqCj49Pc3Jkye142bCpDeCQGA5VQctsxkZmPYzMOOn3G7Ebop/RWqE4ff72bt3LwcPZpUAz0MqeVWzBHUFNBgMGW9yIQSBiILZIC8oGlHRXG7lli1FPHjCQ2OpmQKTnvdc2si+5pJlIZPa/6x+t+rEFZUEC7WIpn6+sxWiLwWJ1k6qe656P4RCIYqKirTvYrF78FOLUtZecEmSioH/BK4WQgxJkrTwdI5TWBGCq/O6syWdFEWhp6cHt9udJAhJXInL7Ea+fvPWnM6pEtwTiNDe1QfBuZyMG4stBhRFEFMEOlliyhti3B3kO3/uQy/L3LannpZyM0ePHqW0tHRJfnGQPD54aGiIiYkJGhsbmZub0/q2FUXROq/Uc0y4g9z73AgzvjA2o463X9yQs9nhxY029jUVU1harnV2rRRSJ66oNemOjo6stXdYHBnnAhF+eXQSpz/MzoYiXtVSmvZzrWQvuNFopKGhQVMRqt1xDz30EN///vepq6vjz3/+MxdffPGCCbtTC8VCveC3AQ8LIYYAhBCOXK93xQieTVMeDAY5duwYZWVl8zzEl9oyqtPpeG7Yz6f//AyyrKOi2M4/t8RYvcB2s7ncyiUNZo7MhJAkGJwJsGdVMbVFFgKRGD/8ax9XVnrZtml9zpr6dFC3LcePHwfirrHRaDTJMODEiRM4HA6Gh4ex2+0Ul5Ty/cNuIgrUFpnxhqJ8/9khPnFVixZZZIJyKlow6KRl8S5fDFJr0un2tGo4b7PZcl7BfaEoH/1FBxPuEDpZ4o9dM0x6Qty8c75rz0oSPPG4iZHM+9//fgBOnjzJfffdh8Ph4C1veUvW442OjsLCveDrAIMkSU8T7wX/hhDiR7lc74rswbN1hamhcybP84Wy4ZlwcnSGX3UFqCyxY7damAtE+PITXXz7tm1Zbx6dTsdVzRbefGkzQ84AvzwyxqpT4o5o0M+My0Xz5dupqFjcrK9UqBNG1qxZQ2Nj47x/NxqNWK1WKisrKSoqwuv10j/mYGhimlKzxGzYjMViwRuDaW84I8GnPCG+/9wwAzMBLFKYt+2ooDqzD8VZQeqeNrX2HgqFGJ+Y4C8jUX7X5cKgk3jbnjouW5OcCHtp2I3DE9akwdGYwv8eGuetO2rm/cbnqhc8Fotx6aWX8s53vjOn42XIuaT+pR7YRbybzAI8J0nSASFE10LHX9EQPRFCxMf6zM7OZg2dl7KCj4yM8MLxfnSyjN0aT3oUWeKKtmBEwZJFoaQKc5rKbdQUmfnDySm8wQgB7yy+UJTqykqqShbfi5yIubk5Ojo6NA9ySP/DqmG8apKwfo2Nys5I3DwxFsE556HfGeLnf/ayvraY12yuo8h+OlxXhOA//zzItC9MdaGRSWeIH7w4zYbVtdoDweWP8OLgLP5wjOZyK5trC3Le158p/OEYY3NBisx6amtrKSyr5InjDo709vFbxzgHR3yYdSDrdHz5t9184Y3r2d5QnPT5Ur+vmIgPY0j9BOfS7GExSbb6+npYuBd8hHhizQf4JEn6M7ANODcET13BVU+z4uLieU0oQggeb5/k18cmMOgkXrfKwO6G3ELKxPG8r967nf89eVDry/YGoxRZDJgN2X/kxH5ws0HH3+yo4j9+24bOaKKkqJS37W3AtkA4nA1jY2MMDg6yceNGNRzLei2JxDfpZW7ZXctPXhhFCB1jQT11lVashSaOjPnoHmvj8lqJ8rJ4uCsMViY9Ia3EZzfJuIKCCXeIlgo93lCUXxyZQBECk0Hm6e4ZoorIqhM/U/hCUUbnQsx4w/zHnwYIRRViiuDmnTWcmPAyOhsk6INhXxCLwUBJoZloNILTF+aBZ44jbbJr4fzW2gJspngbqlEvEwzHuGZzRdoH1MuF4Hv27IGFe8F/BdwjSZIeMBIP4b+Wy/FXJERPXMHVvvBET7NE/PaEg3v+2IfZGLf7/c/xOf5RryP+YMuM1PG8kiTx2kY9L7iiyFJ8KubHrlq34N4uUVo7OzuLa7CDT1+/Cb21kAKTPuvqnw2q1DYQCLBnzx5CodCSSmCtdYV8rNjMiCvIr45N0FIRn7hRXmRjbC5I47pqjDE/DoeDaecsXm8MI1EKrWYURaAIge3UZxibCxGIxDQdtlEnc3SBRpAzwclJL597vJtQNMaQM0ihRU9dsZmoIvjR8yOUWA2sLrMyE/Fii+pw+SPUFMfr7wYDrGuuYe3a0qTxyO/dauN3wzG8UZm9q0t4y4709l9naw+eCr/fvyiCn9IPZO0FF0J0SJL0BHAMUIiX0tpzOn7OV7IIqATv7e1lZmYma1/4E8cnMRlkTegfCIV5bsjD1XsyH9/hcNDd3T2vAeWyOgN3XL2NuUCEmkIzdvPCH0/NvvcODHKsZ4R9O7dSXbr4OnEiIpEIR48epbi4mO3btyNJkuYwmw2Z6uBlNiMWgw6bSZ8cjgrijicl8RbKdUIQLp7gR8+PMO12EonG2FdvxhDxEosZ8IWiHB6e48iIm8ZSC81llpzMHJYCIQRffrKXqKJQYNajALOBCGU2YzyqkiTCsdOftanUgssfYcYbRpIkii16rt1UgdVqwmq1Ul9fr3mT15c4cTqdSNIEI0NhzcYq8WF+LlfwxQpdFuoFP/XnrwJfXdSBWQGCq1/y4OAgVVVV7N69O+sXbdLrtIF6EHchMWa459R9fLrxvCoqC0xZnUfT4eT4HP/zJzdRycA3jx3jPZet4tY0JhG5QO0qW7NmTZIQ5kxFLFajju11Bbw0HO+1DkTie+hEXYAkSbxmYw0t1cVMekL4XVPU2iRcLhcd3X1861iEMa9AkmW6HD7WV1n56OvXLPmasiEcEzj9Ecqs8VvMqJMIRQXhmIJejv+5qsDIpCdEKCLQ6xVu3V1LdaEJo17m1S1l2lQXFYne5M3NzUQiEZxOJ2NjY3R2dmK1WrVw/uUSoq80lp3gqhF8cXFxTg6nf3tRA//3l8eZ8YYRCGxGPZevmr/aLzSedykIBoMcOXKEH59UCGPCZtIRVQTffWaQHY3FbKheXHLN4XDQ09OTtqssF4Iv9Jor1pVTWWBi3B2i1GZgW11h2v1nQ4mFhhILQ7gxmUxUVVUxpXMRpIf6IoEnGCYSVRic8lIkBYhGzfHRzUJweHiOjkkvNoOeS9eULPphqUIlsMsfodCsp77YRP9MkEhM4BMK79zXwKvXlvGroxO09Xp53Y5artxYsaiIwmAwJI1X8vv92pZQXUmNRiMlJSXLZu8Ui8Wy1rZ9Pt9iDRdXFMtum+xwOFi7di0ejyen92ytK+Tf37qVP3VNY9BJXFRnJuZJtpqanZ3l+PHji/J3WwiqCKNl7XqcfzhKeWH8BtDLEmFgYMafluCBcIxpbwh3+LQCSwhBX18fTqeT3bt3p70BlkOGqpMlttYVsrVu8e8Vp6yTLGYjFrOJqCJw+ULMzs4yODCAXq9nJGzl6LRCVZGVWV+E+w8FePtF9Uuqo0uSxCeuauGzj3cxF4gikPi/V61hZ2MxRWY9xad67+/Y18AL+gn2bM5ZnJXxfKqNVWNjozYbfHZ2lv7+/mWzd8pldPAFS3BJkti4cSNOpxOXy5Xz+9ZW2ll7yonE4/HQPxvPwAuR+3he9fwLhWaqjfNLveOU1jUzFTFQaERr+I8p8bJLXRqf87HZIN/9Sz/+cAzHVJhY6QRXbizn+PHjmEymtC4uidd2piv4YpF4rK11hRRZDDhP+dWFooLrtlazbm28bBcKhfjDH7rRhQNMT7gwm824FQMDU162NS5NA9BUZuW7t7bi8IYoNBsozCEnspxInA2eau9kt9s1G6vFtIcuZLjo9/uz2kWdbZwTJdtC71UURRvvI8vyvHnembDQpFD1mC+Oh2lz25FnpxECtlfoaHfLhCIKUUVw6546ttbNT7T99OAwMUVQXWQm4pV4on2CsKOPvRtXU1eXfVk9FwRPRKFZz1du3MBPXxxj2htmR0Mh+1tPK2BMJhMlRYXECgqwGnWEQiGmJ+fo7e0mNn169Vvs9Rn1MvVZhkKs1OdNvQ9S7Z28Xi8zMzNae6jaLVZcXJx1gVhoDy6EOGdur+lwVurgi4E6e/vgwYM0NDSoQoCckE0Fp44MKquqpcProbbQiF4nowjBsRnBPbe0EogolFgNaVdvIQQT7qDmOCoJwdyci/Id6xYkN6wseVMx649waGiO8UkfOxp0qKm+igITH8ky/ufyllJ+eXQSbzhGLAYt9RVcu6sWWcS0RhK/38+JEyeWxRwBzs1scFVIVFBQwOrVq5PcWnt6ejCZTNrns1qtSde3Eo6qK4kVyaKnU7LlCqfTidvt5qKLLkqyRc4FmXzVVXns5s2bwWgDTmpGBLIkIRGvCa+pyJz9lCSJVaVWxueCGEWIQDhKcXEpTdW5TVM5Wyv4tDfMp359ElcgQjgU5oleH18sLqOxdOGwcW2lndv26Blw+rHodWyssZ9yG9VpjSRer5f6+nrNHEFRFC1znVqqygXnw2zwVLdWdRZ6X18fgUCAgoICysrKKCkpyclw8Xwi+XmzgieO57XZbIsmN8xvGVX321NTU5o8VlEE9SUWRl0BSm1G5oIR7IbsQ/1U3Lqnjq/++iVGAzGEZOTm7dXUl+S233IHo0z7Y3iDUexmPX6/n76+Pq3LSm0XPVOC/7ZjirlAhKoCEwFdDHdY8MDhcf7pdennlqeirthMXQYPNfXmTTRHUL3O1FKVzWbLyaI59ZjLjTN5cFgsFurq6qirq9NGSM3MzDA8PIzP58NoNFJVVUVBQUHSOZby2z3xxBNcc801J8nSCw4gSdIe4ADxoYMP5nr8FSH4YmeMpY7nfe6555Z03sS9f+J8scRavCxLvPOSVfziyBj9M36aymw0Fs1qI3+yXWN/xzHee3ENJZW1dHUcp3VVcU7X1THu5umuGYbHooy/OMLeGiPeiX5WrVqFz+djZGREu/7i4uJ5N30kphA+ZXhhSDNBJRHuQBRdwmsMOmmet/lyInXiitomqlo0l5SUUFZWltHT7XwkeCISR0gBHDp0CLvdztjYGB6PB4vFkjRrbTGDPmKxGB/84AcBriHzXHCk+Pzwu4mr3RaFFRO65Ip043mXCvXBkjgyKN3+uMCs5/aLT3d0Pfts9qkjc3NztLe3J12j2ZDbQ8wbjPLn7hkq7AZ8ZomY381Dz7v46P49GPU6KisraWpqIhwO093dzfT0NJOTkxQWFsYFG0Y7zw26icQUDDqZy9eUzhOAJGLPqiL+1DNDIBIjHBMEIoJ9TcULXmc2dE54+b+PnGTCHaTBJvjWxnDaa0htE1X3tqry0Gw2J81Tg3MnKV0qhBBUV1drJpXqCKnDhw/zoQ99CEmSePTRR7niiisWFLwcPHiQlpYWent7s/WCA3wIeAjIou9Mj3PmySZE5vG8S4UsyzidTsbHx7P6qDt9YX7w7CC9Uz5qisxsN8cdUiMxwfhcEJtJR/kp3zK1WSS1TJerPbQ/Eo8o9DqZSCRCJBSgprYedAbisuI4jEajNi64uroat9tNx+Akv2zvpsSso6mqCGG28ueeGd64tSrjSr57VTHvvWwVDx4eJwzs31jMlRuXrh1w+sK84ydH8Ybin6MzDO/+2TEefndcbDQ6G+TggAu9TuayNaVJ3vKJe1vV021mZkbz3isuLl4x1ddKElw9bmLtvaGhgZ/97Gd85CMf4S9/+QsHDhzgC1/4QtZjjY6O0tCQpJic1wsuSVId8CbiY4NfHgTPNp53qVAtf6PRaEYZK8RHEX39D72MzwYptRsYnwvSPRRh01Yv//Lrk0z7wsQUwZt31PCaqjB+v589e/akNWvMheCFZj2yJOjs6UcCCsur0etkLAYdsWhyBJDYLnpsKspXnp3DF9IhAZfKYdbYA0zMBTkmu2isqUhrdgjwmnVlvGZdGYODg5jN5jMKgY+NJguWFAFDzgBOfwSnL8L/98sOgpEYIHHfi2N8862bM67uVqsVq9VKQ0ODZgIxOTnJ7Oys5phTVlaGxWLRrnlsLsh3/jKIwxNmR30hd+xrSDJ0nHSHODjgIipgZ0MRq0pXNjLIhmg0SmNjI3fffXdOr8+xF/zrxAcNxpbyO65YiJ5JdJJpPG8qFrM3U0cGCSFYs2ZN1tLNbCDC2GyAqsL4XqnUZmTaCV94vItJT4hCi55YTOFnBwaovKSCmy5Lb9GUa54hFg5SExkjVFjM2GSEVXqZqzZVoZMlwrGYVs5RzfSFiM9C+7en+jHpZKJ6AULw7FCALZc2sKZUoqHOjHvWxcApBVp5efk8YiwXbCYdipJ8zykCLAYdPzzQRyQmKLHGv+9Zf4RfHZvgXZfMN7RIhWoCoSbimpqakrrGzPZCBvxGvnNwimgMLAaZAWeAKW+YT12zFgCHJ8R//KmfSEwgS/Bsn4v3X76K5nLrOSG43+9fVKNJfX29Ztel/hXze8F3A/ef+l3LgWslSYoKIX6ZyzlWbAVXE16JX3Km8bypSFzJFkLiyKBgMLgg6dQhc+qeVjmlXBubC2Az6VFiCsFAAFnWoVjT+30lXmM2qLroV+1u5Vp7AX/+67O8ene8KyoajWrEVq85Go0iSRIz3hACMBlkZAk8oRgxoTDhDvPWnTVUFpmpLCtlzZo1mjtKb28vgUCA4uJiysrKKC4uXvC7ywU7G4rYWFPA8XEPwYiCSQe37a3DatThDkYx6E5/P1IOY4pSof7OiZlrfyjCV3/bxZHRSSbnIuhl0NsM2I16nul1agnHFwbnCEcF1UXxh4TLH+GPXdM0lzeeup6zW65arOHinj176O7uJlsvuBBCEy5IkvRD4NFcyQ1ngeAGgwFFUTh58iTBYDCtN3mm9y70BE4dGTQ4OLggwa1GHW/dWcf9h0aRiHev7awyMhiy0D3pRU8Es9lCLCK0vmmIDwtsG3MTjMS0nuxs5xoaGmJ8fDzJvcaoi79HHdWT+D1MT08zMTHB5s2bEbKMUSfhC0axmfRYDAKDTuJvdtXO82tPnEyiKAqzs7PMzMzQ19dHLBbTSlpLzXHoZInv3baVXx6dZMjpozDi5M5TYplXtZRx74Fh9Ke81wEuaVqcrDXdVJO2cS8TfoX68gImfHNICNyhGLKIEY4onDzZSVVFOeFIBCnhrbJEUmficmOhB7oqgc0Ver2ee+65h+uuuy7bXPAzwoqF6Hq9nmg0SjAY5OjRo1RWVrJhw4acnqqJD4d0EEJworOLAccc27e2YrfHn5q5hs1Xba6iqdzGuDtIqdVIeKIbLybunpojpjMTiAqu2VylmeOHowpfe6qHk5NeJECvk7ipRU9FxfwfXB20EIlE2L17t6Z6EkIQi8W0p3zi9zAyMsL4+Di7du06VatX+Ox16/js4124g1H0ssTHX7+aMqsua+gpy3JSyeZ4ZxdzgQjHO04iYpGk1X0x4atBJ/PWnTWnjCG92rW/eUc1gUiMR9sncfvjvd6PtE1SZNHn3ImXbi5ZMKIgSxLlNiN2UzxSiAmIyQb+9uIaGuuLmJmZweSZxjkTJeQ3YrGYCcUk9u04M++8xV5rIpbSKnrttdcihEhqu8xEbCHEHYs6OCu8gjudToaHh9m4caN20+X63kxCmUgkwp8OHuFnnRHCkpGf9nTyho0V3LGvEZ0urqHOBeuq7KyrshOLxfhLt4fSUgMPfOAyhl1BbCY99cWnk1OHh2fpnPBQWxT/O3cgwmNdXnY2JxNcNXooKSlJGrSgkrupqUnbY6r14enpacLhMDt37tQeBrIss7W+mPvetRunL0KhWYdeEppGX/1uZFlGkqS0ZG0f83DvES+SLFNSaONtu2sokEKaHFMtWZWVleVcu03dNsmSxO0X1eMLxTgx4aGq0EQgHOM7zwzxyataqFhAPNQ+5uGXh8cIBQLcXnx6nNKaCis6Ke7htqexiOMTXqoLTNy8q5bXritDkuIjlpqbm2lZN8cTx0Zxe31sL4igm5WYkEuXZNy5EBZqNDnfesFhhQiuivnn5uayurlkQiaCq8MDnxo3E5Ykyu0mYorgt8cdbKsvota4OIFNIBDg6NGjmM1mmpqasJkMbKieHzUEIoqWBAOwGHVM+UTSuXw+H0ePHp1n9KCSW62f1tTUoCgK09PTdHZ2EovFKCoqYnx8nPLy8qTvyqCT54Xkaoiv/qeSLpHsc4EI//vSGHajhM1sICZJ3Hdogo++YY3mbJrYOx2JRBYUpKiY514qBCcmvFQXmuJlI5MeTzDGyGwwK8GPjrr53OPdxGJRotEYnY908sUbNrC20kZ9sYX3Xb6Khw5P4AtHuX1vPTe0pi8NrqsuYl11kfZdq6qzYDDIiy++eEYy2lTkYvaQS1/C2cSyEzwajXLkyBGEELS0tCya3JCe4GqCrrW1lXt7u7UeZZ0sISSYdAdpqMrNctkbjPKTZ3s41DNOS30lF5VHs76vudyKLMUNBE0GGYcnxJZKs7YnU4mydevWJIlt7FSWHEgiTTgcZmBggDVr1lBTU4PP52N6eprjx49rXunl5eUUFRXNuyllWdaOpRI8kfDRaJRpdxBFCKynykmFZj3j7hC+UFT73lJLVi6XSxOkWCwWbXVPlJumdYIFCsw6/BEFm1EXvx5E2lnbJye99E/7KTDr+W3HFDopnqWP6SEg4PHjDj5cGd/fb6opYFPN4vqqE2W009PTbNu27YxktKlYiOCLzaKfDSw7wfV6vTaxY6lhUmJXWOrIIL1ez+pyKx3jHm0Fl4CaIguyHF1QAy+E4J7ftdE5Osvahio8EXi400fLqggZdDE0llq564pmfvL8CHOBKJevLeOSijh50yXTEkmXuPJDXBV34sQJNm7cqGW6VbHEqlWriEajzMzMMDo6qlktq2Ww1JyESnT1plPPWWSNgRD4QxHsOhl3MIJZL2UccK/T6ZIEKerqfuLECa2Vsry8PO14JUmKe5h/75khPIEIioBdjUXzppe+MDjLo+2TmA06IlGFk5O+pIKvmvBcDqj3TjoZrfq5otGolq/IdTTyy83sAVYoyVZeXo7P51tyR5naFRYOh9OODHrPZav58hPxurUiBNdvrWZbfSGzs7NZHyqKonC47TjdE142N9Wi0+mwmMDhhPG5IPVZZglubyhO8uju7+9nZGQEs9k8L5mWidyTk5MMDAywffv2jFltvV6fZEPk8XiYnp7W6qUqEdO5kqire2WRjctqZB7tiCCMNozEuG1XDSgxokJJigJSkeqMEo1GtVVwbm6OWCzGxMREUqvo5poCPnFVCyOzQWxGHeuqbElWUlFF8MeuaSoLTJpIxeEJ0T8TICoLYoqC0QBXbVq64s4XiuIPxyixGZHSZOYTZbTqgzQxakkno03Fy82PDVY4yRaJRJb8Xo/HQ3d3d1qbpooCE1++aTNTnjBmg6xNusjWDx4Ohzly5AglZeWUlUnEhISO+B5SCFjAPj0JkUiEkZER7HY7W7duxReKMeXyoZMkKgv06E4ROzHJ1t/fr+UkFioTqkgMOZubmwmHw0xPT9Pf34/P56O4uJjy8nJKS0uTVvHOzk6aCuHLf7MXX0Sh2GLArJe0LUPHuBt3MEqF3UBTuT1jog7iDxx1hPCh/il+9KduYr3DrC8c4PJ6PeWnQvnKgoJ5+YJAJMZfe52MzAY5Me5lY7Ud0ymVW2WBideur+CF3klQFP720hY2Vi+NHH/smuZnL8T1IcVWAx96VcOCK3Li50qU0Z48eZJI5HTFoaioKOm7XW5H1ZXGihFcr9cTDAaX9F6Px6NNQMn0hRl0clKdGjL3g7vdbtra2rSHxY3M8OBL8RtCINhcaaKmIDffMTWZps6KnvGF+U37JJGoQkRRqC0y8foNFRj1p/fJJ06cQK/Xs23btow3Xjim0DnhYcYbocxuYEN1AcaUpJLRaJxX856enqa3t5fZqJ5+v5FZt5c9TWW8bmfcEz5x1yFJEg8eHuOvvU4k4g+3G7dWsK+pRJvomml1H3IG+NrTw0TDUFxo5gVnhJraChqtRm2iqNo3rba/HuifZWQ2SHWhiXVVNo6MuNlWV4ggPh/9yo3lXFwZj3bqa5cW2g45A/zk4CglNgNGnYzLF+E7zwxxS1PuriqZZLSpBhDAggS/4EN0WLrpg7r6+P1+GhsbF/00TFcHV5Nz27dv1453yZoyaostjM8FKTTrMfodOenKVeOI1tZWLVw9OOBCL0sUn3pAjM2FGJ0N0VRu1Zxgq6qqUpsKkj+3EDzb62TCHcJu1DHhDuH0RXjV2rKMY4USa96T7hD/9XQ3btc0ep3MI8cmCYcjXLy+NqnmPe4OcaBvlrpiC7IkEY4p/KbDyb41FegWKMO1jcU72uzGuI5eluDZgTlu3bslaTsxMzPDyMhIXE8/qae+oihui1VfSCQqMBtkVpdZeVVLKXaTnrkltouGowp/6p7huX4Xs/6IlrEvtuoZnQ0gWPrAxdRZaqoBxOjoKJFIhFAopBlAJBJ+KSH6Qv3gkiS9DfjYqT96gfcLIY7mevwVV7LlilAoxNGjR6moqKC4uHhJq39iiC6E0Awk0qnnVpdZWX1qyGB//8yCCcHUZJrH4yESieALRjDoQEICSUInSwSjcUFLe3s7LS0tC7bB+sMxJtwhqk7dpDaTngl3EH84tuAUUYAjA1O4XE42NNZitVqY80cYDoRpmpzk5MmT2Gw2ysvL8UhWJAntoWGQ47O9IgqYzXFCqJn5xApANBrFICdn0SOxuMW1isTthNr+2ubtZ2RiCjkWxmIxU2K0cNP2OupLTz+40ynZFoIiBN/96xDHRt3EFMGEJwQSrKu04wnGKLcaMOiXzxdNldGqn99mszEzM6O5tZaVlWkipsUQPMd+8H7g1UIIlyRJ1wDfZf700YxY0RA91xVctUVWJ446HI4lebqpIXo0GuXo0aMUFhbmNM87mwJOURQ6OjqIxWJJnW+SFN/Triot4PCwm6oimUhEAQG6sJf29kG2bNmS0w+uXp1a044P2ZPIZWFzOp2MDA9SWlaO9dTgRQUoKSpg48Y6LXs8NTXF1OQovrkggwEj5UV2PGFoLLFiN50mQ7rMfCwWY8+qIh5+SWZiLkJABJFlifdeljkqMRqNXLezid92TBGJKvgDQerNYcZ7TzA1eHp8cCwWyzknoWLSHaJ9zEPNqdp7LCbomfZTYIpHZO/YW4UccC7qmLlAnQ2ujguG+MI0MzPD5z//eXp7e/nIRz7CNddcw0033bTgfZdLP7gQ4tmEtxwg3pCSM875Cj48PMzIyEhST/iZzAiPRCIcPHiQ5uZmqnOcm5uJ4GoWv7y8nNWrVyclzcxmMz09PdjsXhptNia8ISwmPZuLIsyd6nHP1ZDQatTRXG6l2+HDYpAJRBTWVtqSVshUKELQ0TeCyzHGDZdt576XJhmdDaGX41nrPauKeeLEJEPOAKtLrbx2wyqamppobPHwo2f7GZ2Zo9wY4+KSYhwOB2VlZWmJpu7JFZeL29YozFpWEYrB1lo7a8qtRCKRjIq6cruRN22rZjYQwaiTKbPFy2wqKQYGBpidncVms6HX63MeUKCI5Gmiq8os6GSJD7x6NRuqbEQCXhyhszPVxGQyUVtby/e+9z0uu+wy3vGOd/Dcc8/ltO3IpR88Be8CfrOYa16xPfhCvmxq8klRFPbu3Zv0xS3W8knFzMwMPp+Piy++eFGebrIsz8v4q11qLS0tVFaeNuVXw1e73c7FF1+M2+3GOjVFUXiKsC+MiBjZtHkzRqORaW+YKW8Io05mVZkFfZbS1O5VxVTYjcwGohRb9NqM8nQYcfn5x58fYdoXwWQycVeBl7df3MDxMQ8RRWFdpY2fvTDK8wOzGHQSv49Nc2LCy4df00RjeQGfuqFV+yxzc3NMT08zODiYVA9PdBMdGRlhcnKSyy7apdXi04ls0iXqrEZdUv19ZDbA4EwAm8nOlk01DA8OIEmSNqDAYDBo+99MPvhVhSaayq30TvuxG3V4wzFa6wvZ0RCf9OL0nf2xRepW45JLLuHSSy/N6Xg59oMDIEnSa4gT/LLcrjaOFV3BM4XoagNKdXU1jY2N8552izVtTDRXtFqtS3JjTXygJCbTErOiQgjtM8myzOhskLufHKZ3yodNinDnrhJW1RTS1dXFkCvAkdn44DyD0URzuZXrtlZlJLksSTSVL5xUVBSF/+9/X2Lar1BWaCOqKPzH0/2sq7RzyZp4pndsLsiLg3NUFRi1kP/5fhdTe+qSzCUlSdJmfUH8d5menqa7u5tgMEhxcTGRSIRYLMb27dvnPYRhfiifLVF3ZGSO/3pmCCHi3+XWukKuqlMoKS7S8hTBYJCZmRlNs5/YIKOeSy9L3PXq1TzaPsmwK8jqUgvXbqnUcgvnai7ZYv3lcuwHR5KkVuC/gWuEEDM5n4AVJHimVVgdGZStASVTuSsdYrEY7e3tGAwGdu/ezYEDBxZ1nd5glO8cmOTEuIe1NQHetM6E8DmTXGHSiVeiisI//7oThyeIIRYkoDPy/bYg39u2nsbGRo78dYDyIj9K0E/AOcPBaSN15gjbmmsydskthGg0yuEjRxn3CsoKLEhSvFwYjCgMzPg19VhMEUn7d4l4r3Z0gVZKs9lMfX099fX1xGIxjh07piU729ratNU9nfw4nYQ2MVEXi8X48fMjFJh0WI16hBC0jbpZazWwu0RKuoZER9PE9lej0Xh6dbdYuHlnesMQleDuYJQnO6aY8YXZWG3nsjWlGasSuSCbkm0pjqq59INLktQIPAz8nRCia7HnWLEQPfVJJoRgaGiIiYmJBRtQct2Dq8MD6+rqspahMkEIwb882sGRITdGWfBcr4P2YZmfvntfVnIDzHgjTLoD6GMhrDYbel28rXHYGWRzrYFQDCqKi9DJxQgEA4453F4fhw8f1kLhioqKBccxJX5W1UiyomgEfziG9dRMdQFUFpze79cUmVhVZmFg2o/VqMMXVlhbYdOy9AtBfWgWFhZq448Xq5eH5NU9Go3iC8cotxk00ktSfNZbru2v6Tzd0rW/KopCWIF/e6oPhzuEySBzaGiOaW+Ym7annyeeC7IJXYLBYM6/pYoc+8H/GSgD/vPU9xwVQuzO+RyLuqIlInUM0ULhUy4EV91YN23apGU0F4vZQITjYx4KTTqCwQBFZhMR9PRM+9nRYMwqO/W6pgiFQtgKrPgjAo8nSCiqMOj0s6nGzoYqG0dH3XF/8oiC1WJh56Z6ii0GLRQ+efIkoVCI0tJSKioqMmqiPR4P7e3tbNiwgZKSEj59jZVPPtKJPxwjGhNcu6WS1oRRS3pZ5hNXreW+F0YZmPHTXGHj1t112rCHbIhEIlrtPnGqTKpeXq0Ld3R0YLfbtdU9XXQiyzJGo5GdDcUcGp6jwm7EH44iS1Csj2iVj2wSWoiXqxIjjEQxSmL7q6IoDLujTHlCmttLoVnPUydn2N9andP3kA7ZQnSv17togsPC/eBCiDuBOxd94FNYcYKrI4Pq6+tzXmUXIvjIyMi8zPtSYNTFtxGBSBC9TofJZCIUjGLUyUltnqmy076+PtxuN++/Yi3feWYIXyiKXiezvaGQ3ikfPVM+Lm0pQ5Yluh0+bCY912yupPhUJ1dqKKw6wXZ2ds4jy8zMDN3d3bS2tmpCna11hfzw9u30z/gpthhoLrfOW0ULzQbee/nqRX0fqhZh9erVSYnFVOj1+qQmjhGHixMjDnydQ1RaJaoqK9Lq5W/f13BKNDNHkdnAVfWC+jIrJSUl2vedS687JItREqWmHR0d+P1+5iJmwhEJIUzaduVMh0osRPDzTYcOKxiiQ3zP+NJLL7Fly5ZFeYRlsiROdEvJNpAw12SH3+1id1mUAw4jwUiMsD/C9oYi1lfZk5JpKtRIxGQysX37dnZIEs5glL4pH9WFZuqLzbj8EUZcAdZW2nn12nJevTa7yEWn0yVpotXmksOHDxONxrvjtm7dOk/VV2ozahr85YDP56OtrY3169cvKiIamwvxq45ZYooRRZQT0hupM8iaXr6oqIiKigpKS0uxGfW89/JVKIpCe3s7dnsBTU1N2m+Vae++ENlTpaYDAwPY/UGsI266hh1YjDqikoFrtlQtefVOvJZ0OB916LCChg/9/f2Ew2H27du3LB9crUmXlZUluaWkQk3uLZTtHBwcxOFw8C837+MPHZMc7Bplx/rVvGFjOUKJzQvJ1ekrNTU1SaHr+ko70ajQGi1CUYUC89KSaKoarKCgQCthVVRUMDAwoLnAqEq/5cwSqy2sW7ZsWbSW+umuKaxGPXaTjt5pP092zGAyVHNDayuKomhluN7eXoxGI6WlpUxPT1NZWUljY7L7auLePZHgiWU49d8zfX5FCI5OBOhyKTTVlFMbVTDKMeosCmtkBy++OHlGJhCZzuv3+185K7jb7dZKHMsxStXj8XDs2LG0nWWpUMP7TOdV6++ANtLo8pZSaiUXW7ZUpt1vezwejh8/ztq1azV9soqdjUUMuwKMzcWzzRV2E1uW2DihXl9HRwc6nU5T4aWaMqjy04qKCsrKys5owqe6h83WwpoNvrCCzSjzaPskx8c8RBXBkRE3Dk+IOy9dpam+1q5di8fj4ejRo+h0OsbGxggGg5SXl6d9YJ0eNXU6M59YgssUyp+c9HFkPEBjmZ0Cu4Uxd5DXra9i8ynzCDV/oJpALHVOeCoW66h6trAiBC8uLsZqtXLkyJEljxFWMTExQV9fH9u2bcvpCZlNJKO2jFZWVrJq1aokD/dwOJxkZaxiampKc25N9wPajHrevKOGSXcYSYqrt/zhGDpZWnCOWCpUf/eysrJ5+oBEEcqLgy5+3T6O6BtnZ8kQFVZZy8qnGjpmw/j4uJbLWOrNva7SxlMnp2gf9aCc2hoJBN99ZpC37KzV8g7hcJiOjg7WrVtHZWWllnuYPKWXt1qt2udL57aiJuD0en2SyEa9v1SRzYjLj0Unodfp0MkSBSY9I7NBjeCp+QN1TnhbWxuAtroXFBQsanU/H3vBYYWTbGcyJ1xtFnG73ezZsyfn2nEmgqvKtLVr1yZFAUIIDAYDFouFF154gYKCAm3POD4+jsPhWJAAJr2OxlIL3Q4vb/+fw7gDEYx6mf979VoubsrNbFIV/6xevTrJ0y0Vf+qe5u4ne5CBmIAjUzr+/U0b0Ic99Pb24vf7tVC+pKQkY0g5ODiI0+lMMntcCi5ZU0rXpBdJijfcGHRSfCSzFB+EqFYNjhw5khQBpeYe1DJcW1sbiqJoZbh0YXRiKK/acqsJUatBxhcKI0R8xQ+EoxSY0n8+SUqeEx6JRLQ56OnaX7PhFUnwpc4Jj0ajBAIBFEVh586di3qSpsvAT01NaZnoxB9BTehIksTGjRu1JJfD4aCjowNZllm1alVOD6lITOGTv+rEG4pSYDYQisT4/OPd/M/bd2QcFhhTBL86OsHRoRkMQRfvft1mqsqzPxDue2EUk07W5J8zvjB/6ZvjbXvrtT5xl8vF1NQUXV1dWK1WKiriWW2j0ag9OMPhcNb+9Fxh1MncvLuOHx+M1+alU99Fud1IdZFJS95t2LAhY6JVkiRMFiuDYTvTOiOry03YzBGGh4fxeDwUFhZqxhaZynDq5yjDTYlFx1xEx+xcgDKrkS1V1pzKcAaDYZ6bjtr+CvE8jMfjSeum84oiuPrhl9I0ohoqmEwmmpubl5QESWwZVZNpu3fvTlqF1eRN4v5NnbDhdrtZtWoV1dXVTE9P09HRQSQS0cLgdOGb0xfBE4pq7Z0mgw5/OMqwK5CR4F/4TRdPnnAQiUYxGvSM/m6Ee/6mJGumd75KTUoy+5dlOal8pK6MR48e1cJau93Opk2bli1RV2wx8O1bW/n/fnGCSXeI1WVW/u3Nmwn5fbS3ty+YvIspgq/8rocjw27Uj/62vXXc0Lplnl5elmUtlE/cjggh6O3tRURC3HXdbqY8YQRQYTOgk0RSGU4IoW3FsmXmE9tfA4EAR44cYXBwEJ/Ppz101PlwPp9vXn5mITzxxBN8+MMfpqurq4f0veAS8A3gWsAP3CGEeGkx51jxEH0xK7gq/tiyZQs9PT1Zhx9kgpqBTZdMg+yeaX6/XxuDpIbJDQ0NNDQ0aGaIQ0NDeDweiouLtVBelmUKLfq4icKpsToxRRBTyEjuGV+YJ09MIosYhdb4nrNj3MPJSW9WN9E3tlbz7T8PoCiCqCIw6mUub0l/YyX6kDU0NHDkyBEsFguKovD8889rnyHXLq5s2FJbyOMfvFgrUcZbgDuT6veZcHLSS9uoR9POR2IK9704xjWb41bJqXr5mZmZpO1IWVkZTqeTWCzG5s2bkSSJ+pL5CcNMve7qyp7tgafT6bBYLGzZsgVFUbRy5uDgIM899xwvvPACdrs95xKt2gv+u9/9jjVr1mwifS/4NcDaU/9dBHybRfSCwwoSXHV1yWUFT11pTSbTkltGZVkmGAzS3d2dlEyLKfEBdZnI7XK56OzsZPPmzWmbVRLNEFWN9NTUFD09PVgsFioqKviH16zi3/84QDQsiAnB311UT0OaG00IQXdvH0JRMJmMCcm+eHibDfHRwRK/75jGYpT5270NNJVnV1CpJcb6+npqauJSzdTPYDabtVB+KZbCKiRJ0sQ527dvz8k2OxRVkKWEqThyvEEmqggMKc8dVateXlXN+GyQgNetbTmKiooYHR3NqpeHxTXIqEiszMiyTFFRkTaeuqqqioMHD/LQQw9x7733cv/997Nx48asn1ntBW9ubkYIEU7XC37qzz8ScVHIAUmSiiVJqhFCjC/4pZ7COd+Dq+IRnU6XtNJmM1DMhmg0SldXF5s2baKiogJvMMovj47TN+XDZpS5oTU+tiiR3GNjY4yMjLBjx460N4Y/HGPIGUAnx51gDLrTGulEQ4Ui3zQfbpUJGQpoqatgU8N8kYsaWRQZ9WyqK6ZzwotepxCNxWvp66qy7+MkSeKazVVcszmLBWwC1OEOqc4yqTpv9TMkJrkybUeyweFwMDAwsKjM/JoKK1ajDpc/jNWoZy4QYVt9IZZUdp/CtDfMt/7Uj8sfZm7Ow7ZqMx+69mKCp9RsJ06cIBKJUFpaqunl063OqQ0y2QZKZBO5NDQ0UFZWxkc/+lH27t27nL3gdcBwymvqgPOD4Hq9PusoITW7WltbO0/0sJQV3OFw4HA4aGpq0jLlvzw6zsCMj+pCA75QjJ8fGuP9r2qi2GrQ9m0+n49du3alDVOdvjD3PN3PXDDu+d1UZuW9l6/CdMoSKDEMbmpqIhSKjweamhrhwGiPpjMvLi7WymAVFRU0Njby76sjfOMP/Rwf97Cq1ML/ef2ajDf1UqBq2Ddt2qStNpmgas3VbPLMzAyDg4N4vd4kNVq2UH5sbIyxsTF27NixqK1VodnAv1y3nu//dQiHJ8Sr1pZxx8WZZc0PvDTKXCCCIeKj3K6n26vn+LiX1rrCJLvndBLgTLqBhQZKBIPBeOtthlZUNcmW6+fOsRc83ZNiUXrbcxaiqzZNmdpGF9MyqvaDT09P09jYqH3JMUXQO+Wl+tTezm424AnFcHhCFJhk2tvbsVqttLa2ZnzqPtY+iTcUpaYwPsmkb9rP8/0uXpVBgmoymbR2x0SdubqqqK6oEL+xP33turTHWSwUIfj5i2P8oWuKYouB27aVEpoazLgHdnhC/K5jCl84xo76QnavKta+A4PBQHV1NdXV1ZoaTdUDmEwmLZRPjHaGhoaYnp5mx44dS9rPN5RY+Mz163N67agrSMzvxmg2UlRURHA2yIwvnPSa1Hq3umc+ejTuV7iQvzycDuVDoRD9/f00NTVlDOUX66iaYy/4CNCwwGuy4pwk2UZGRhgeHs7aLJLrCq4oitaptmvXLkZGRrQnMELBapAJRBVsRj2KECgCdMQ4dOiQRsRsmPGFtZKUJEkYdRJOX25+72qt12QyMTs7S0tLC8FgkEOHDmEwGLQ68FLGO6Xie88M8pODIwggGlU40DPFj9+xMy25Xf4w//5UL6GIgkkvc3RkjkAklvahJctykgeZ3+/X2kZjsRilpaWEw2HC4TDbt29fEaOFRCiKgjniZlLRUV1YiKLEfe2ztcKm85dXTRNVvbxahku1rVIHSqpbnEwim6mpqSXNBu/v76e5udlIml5w4BHgrlP784uAucXsv+Es7METSaooitYiuWfPnqxme7kQXFWmVVVVacov1ZdNDa1u3FbDzw+N4Q5EUYRgU4WZyd64wWMuE0/XVdp5smMq3nutCEJRQXNF7m2BiVJQtZ2wpaVlHlHUEly6FSUXPHR4HFmWkBQFSVaIoeP5IQ+rK5IThlFF4X8ODHNoaI5ii57VZVbKbUb+cHI6Y1SSCKvVSmNjI42NjUQiEdrb2/H5fOh0Og4dO063z0RUNrGptpBdjcVL+iyZoCgKx44d48bWcp4YFAzPBkDANVsqFzU0wWg0UlNTow2CVMtwqmVUYjff4cOHaWpq0vIX6UQ2v//97xkbG1tU5KL2gl911VUAHaTvBX+ceImsh3iZ7B05n0A9z2LfkCtSfdkSxxDlMid8IYKr+vT169fPSx6Fw2EtU95cYeN9r1rFlCeMzz1LcHqY1m3bcn7avn5jBXOBCC8MziJLEm9srWRrbW6WUCMjI0xMTKRNOKUSxTE1xSPPn2TKE2RTbRG7WmqzKtFSIUsQi8R7rI0GI8Gokta95OmuGY6OuNFLcfPCjgkv66psFC2yQUYVzFitVrZv304wEuP/PdbB8MwMxCL85qjEGzeX86bdq8+opVeF6jCjyng3rRXM+iOY9DK2HKylMyE1QgkEApr2YXZ2lrKyMi3hm+63+Mtf/sIXvvAFXnjhhQXtsVNx7bXXcu211wKsUf8upRdcAB9c2ieL46xk0dWxv6kGhgu9NxPBHQ4HPT098/TpQgjsdjsjIyPaF15ZWUmRzcacYwyPe4bdu3cvKgFk1Mncuqeet+ysRZaknNoN1eSd3+/PaU+q0+v53kseDvRHEeh4fMjN33qjrLV2aU0lmcwU1PO9YbWBB0+EEbJMNBKj0GzginXz6+PHRtysKbcxF4gQiiiEYwrjs0He+pr09kfpoLZ72mw2TYzUPeXHFRKsrYufMxgK88c+D+utJxZ0gFkIsViMo0ePUllZqXXyyZK0rO2yKiwWC9XV1UxMTLB582b0er3W4JOql//rX//KJz/5SR599NGs8uJziRUneCAQoK2tbZ5MNJf3hsPJiZPEZFqqMk3dE5nNZnbu3Bkfo3sq7JqZmcFkMrF+/folCzpybRxRcwImk4mtW7fmdDMfHXHz/ICLAnNcXRWOKjxwMswv33cR/lPlq8OHDyPLsrZvV8N91V7pxk0lbGxq4E/dMxRbDLx9XwMV9vn7UptJhy8c4+KmUgZm/DjcQa7fWsXFTbn1gKeupCpSs8Kqvn/Hzi0op5KNqgOMqgLLZNWcer4jR45QXV19VmZvq+OvGxsbNdKqU1dVVeADDzzAv//7v+P3+/nWt76Vsz33ucCKEVztCQ+FQrz61a9ekiItdf+emExbSJmmTpwYHR2lqakJu92Ow+Ggq6uLgoICKisrtfBruaDaHallsFzhDkROGSOeymLrpLgdkyK0Zojm5mZCoRBTU1NaHqOkpITZ2Vlqa2tpaGhgDXDtluwrybVbqvjvvw7i90fxhqLMhWI8cXwKlz/KnZc2Ys5SplMTTomVABUtFTaKLQYm3SEsRhl3IMobNlYgSxJySkbb7XYzNTXFwMCAtuetqKiYF8qrZKurq9MEOiuJdORWkVgOnZmZwW6386EPfYiHHnqIubk5/vZv/3bFr28pWDGCDw8PoygKFotlSS6iiUKXUCikPcVXrVqlvSab7FRtclizZo1WE1efxOoN1tfXpym4KioqzqgfOBAIaDLXXLchKtZV2ZFliUA4hskg4wlE2VBt12rtKkwmk2b15PP5OHLkCCaTiZGREdxut9Yfnu2hpZMl1lbY6Jz0MhuIsKnajlEv8/yAi0Kzntsz1J/VhOaqVavShqM2k55/fP0aHm+fxOmPcOXGAl6zbv6eVJIkTQWmVhWmpqbo7OzUZn6pOvOjR4+mJdtKQCV3fX191vMdPXqUu+66i4ceeoiWlpYVv64zhbSAT9WSTaxUu6Fnn32WSy65ZNHvd7lcjI+P09DQkDaZlo3cTqdT07QvVJvUxvpMTSFJ0rwQOBe43W6OHz+ek6AkEw4Pz/GVJ3tw+sNsqS3kk1evzbjHTLVXUhsypqamtO2I+jkSZae9Uz4+/ssT+MMxvKEYgUiMi5tKMBt0BCIxzHqZr960ed750rV7rgRisRgzMzM4HA4mJycpKiqivr6esrKyJVtN53peVXCVLVI4fvw473rXu3jggQdYvz63mn2OWL5SQ+qBV4rgqlPmUgnudrvp7OwkGo1mbPNMNUSEuARwdHSUbdu2LVpTrYbAU1NThMPh+Nzrysqsck1VANLa2rokV81ULNSskIu9krpXnJqaQlEUjez/+vQIh4fdFFsNzPrDDLmCNJVZaKm04/SFWVtp52NXJq9KagNOtnbP5YQaKaxevRqz2aw9tBINL5bTOSVXcnd2dnLHHXdw3333sXnz/IfgGWLFCL6iZTIVi534IIRgbGwMr9fL5ZdfnvT0Tp0ukvj36kSOTLLThZAYAqd2j6UzUVDLYLt27Vq2FSbb95SrvVKixbEq6ujr66N/1EUsIhOJxFV0ZkOYuUCEKU8Iq1HH3+5NTmKpUteleLUtBepWrKWlRYsUCgsLWbNmzbypK6rO/Ez86dTsvFoTz4Tu7m7uuOMOfvzjH68EuVcUK7aCK4pCJBLh+eefZ9euXTlPkFRLMBB/mu/eHfd4zxaSR6PRUy6ddtasWbOs4gr1mlQTBZfLhd1u1xKAW7duXdZEXSao9krbtm1bcq7gF4fH+O5fBjDJMSLRKGFF5q3bKtjeXMX66kKKLKcfUrOzs3R0dOTU7rkcULcB69atyypAmvVHeOilUfocc1QaI2wvDlNaVJDVlz0dVHJXVVVlzc4PDAxw6623cu+997Jz585Ff64c8fJbwVWo2fBcCK4+wdUn6uHDh4Hs5FYnfjQ0NKxYpjXRREEN6dQtgpo1T93vLicGBgZwuVxnbK+0f3sNoZjCY+0OdJLEjVtK2VocZWaqlx7naQslv9+vtXsuh0hlIagdbwttA0LRGP/+VC8OTwi7SUf7rEC2lfL2VeVMT09z5MgRJElKmhqT7mGfWFfPRu7h4WFuu+02vve9760kuVcUKx6i5+rL5na7NWsfdTqFSqJM5Fb3oxs3bjwr+0O1TFRVVaW1+vn9fq3NUgihkWQ5Vr3ltleSJYlbdtdzy+7kEdNqCDw1NcXRo0fx+/3U1dURDocxm83LHhElQt3jb9y4ccEE5bAriMMT0iyqrUYdbWMe2NdAc3OzVkpUtzKBQICSkhLNeUV1+1Efyon216kYGxvjlltu4Z577mHv3r3L+pnPJs7KCr5QT/jk5CS9vb1s375dI4bampcpmTY5OcnAwADbtm1bluTWQlBXmcSyG8Qlp6tWrdL2u4n7RDVJtxT/bbVv3GQyaS4lKwmz2YxOp0On07Fv3z7cbrfmiZZru+hi4fP5OHbsWEaTjVTEjSBO53RUp6pEdWFiN5+iKDidziR/ukAgkPSAToeJiQn+5m/+hq997WtcdtmipvWedzhrIXo6qGOAXC5XWufUWCxGb28vVVVVWhZdCEHbyV6ODDppXL2agNCz0vRWI4WFymBGo1ETgaglH7VGXVRURGVlpWbxlA2J9smJdf/FIqYITox7CEUV1lbakvbYqRgeHmZqakrbBlgsFs29JrFddLl0A16vl7a2tkUl8BpKLGyqsdM26sFkkAlFFN6wsQKbMf1tnOjfFovFOHz4MCaTienpaaanp9NaTU9NTfHWt76VL3/5y1xxxRVL/nznC1YsyQbxPXVXV5eWgU6E6uSi1+vZsGHDPHscdfVW66I+n4/S0lImXB7+92QExRjfX1kNOv7p9WuoKTrzlst0UAUxra2tS96PJtojOZ1ObDabpqRLfails1daCiIxhX959CTHRuNGhhaDjq/ctIlVpcmPQ1X+63a72bp1a9aHjxBC25JMTU0BJOkGco0y1Oz81q1bF+1EGo4qPNM7w4Q7RHO5lb2rSxYcCawoCm1tbRQXF2sPTDXamp6exufzMTk5idfr5bvf/S6f+9zn1CaQs4WXXx0c4gTv7e3FZrMl6XUTk2mpeuZsybSXXnqJZ8cVXnLEqC0yxx1QIxI7Goq4Y1/u0tBcMTw8jMPhoLW1ddnKYKrZvsPhYGZmBr1en+QPfvTo0WURlDzZ4eBrT/VRYtEjSRLuYJS1lXb+/S2nyzzqHj8SibBx48ZF7/FVkkxNTREIBBackgqnRUFnKzuvVmUKCwtZvXp1xtf84Q9/4LOf/azmFf+FL3xhQV+1ZcTLM4uu9mcn7sFTk2kqso7q9Xppb29n3bp19OkCVClzWA3x1cTjDdKHH8ca87Jpy9UbPxQKsWPHjmU1MUg021+zZg2BQEBLbnm9XmprazGZTIvWDqRi0h1KOobZIDPhDmr/LoTQRiRt2rRpSedK3ZIkWiSpAyQSG0rm5ubo6Og4a3mTXMgN8fvr7rvv5hOf+ARvfvOb6ezsXLTcWMU73/lOHn30USorK7VybyKEEHz4wx/m8ccfx2q18sMf/nBFM/QrvgdPzKKrY4gSk2mQXZmmDnxXw7ltoTme7XNhNRmwFBRiksxcvrGUubk5+vr6NIfTioqKJa266tZBtchd6eSWxWLR7HZ37dpFIBCgt7eXWa8fr1xAaWkpO5orMRsW91NtOKVvjyoCnQTeUIxXrS0G0rd7nilSJ5WkNpTY7XbN0ulslN6EEBw/flybWpIJXq+Xm2++mbvuuou3vOUtAGe0ct9xxx3cdddd3H777Wn//Te/+Q3d3d10d3fz/PPP8/73v5/nn39+yedbCCsaoofDYcbGxvD7/UBcX75t27aclGkQD5EnJiZobW1NqjEf6HPy+HEHAnjNujJes648PhPrVEufw+FgenpaC38rKytzqlGHw2GOHTtGdXV11hLKcmJycpLBwcEkae1sIMLnHzvJqMtHJByhyBjjA3vLWFVblXMmWwjB/S+O8pMXRhFCsLmmgH++dj1Wg8SxY8coLS09owTeYjA+Pk53dzcWiwUhxJIdW3OFSm6r1Upzc3PG1/n9fm6++WbuuOOOjIRcCgYGBrj++uvTruDvfe97ueKKK7j11lsBWL9+PV1dXbWLtWLKFSseosuyzPj4OGVlZezcuTNtMi111RZC0NXVRTgcTivuuLi5lIub56udElv6mpubCQQCOByOpBp1ZWVl2vBQrcemlsFWEuoeP9WF9BeHx5nwhKktiSegJtxBjs2ZKLS46O3tzSlKkSSJW/fU8+YdtYRjCjajTssk19TUnJXeakCT+1500UWYTKZ5jq2pAyTOFCq5LRZLVnIHAgFuvfVWbrvttmUl90JItUuur6+nq6trUVbIi8GKElwdQGA0GpPCnoVkp21tbRQWFrJu3bozesJbLJakGrXD4aCzs1MbQ1RZWYndbsftdnPixImc67FnCrU86PV62b59+7wH2IQnhMVw+mY363W4ozrWrWtO8mE/fPhwUmicLvQ16mWMennBds+VgDoXfMeOHVpJLdWxVa0uqPZPiXPUFgshBCdOnMBsNrNmzZqMrwuFQvzd3/0db3rTm3jXu9615M+3FORol7xsWFGC9/b20tjYiNvt1v4u0ZFStZ1VofZUq3PBlhNGo1FrJIlEIprby9zcHIqisGHDhrPSUKEmtyRJymjXvKnaTtuoG7tJjxAQjMbYdMpUMNWHXVWgdXR0aNZI6oNLPbY6uXTNmjWL9g2DuFHjY+0OOie81BebuXF7dcbas4qpqSn6+/uTyJ2KxOELiQ+uo0ePJklOc8m2q9+ryWTKSu5wOMzb3/52rrzySt7//veveI4lFal2yacGGy7KCnkxWFGCb9myBbfbjdPpBJKTaankPpuyU4PBQE1NDZFIhHA4TF1dHdPT0/T19VFcXExlZeWiDA9zhWqvVFBQQFNTU8ab69otVTi8YZ7umkECrtpYyes2pN82mM1mbX5a4oNL1Q0UFhYyMDBwRt/rPU/383TXDCa9zIF+hSMjc3xx/8aMNlaTk5MMDQ0tagBCpgESiapAtQSX+r2p5DYYDFmbjSKRCO9617u47LLL+PCHP3zWyQ1www03cM8993DLLbfw/PPPU1RUxErtv2GFk2zRaBSfz8fx48fZuXNnxkz5xMQEg4ODZyQmWQzUPX4kEkmasqmGjA6HA5fLtazWTqqOfTEJvHA07mhj1C/+QaMoCqOjo/T09GA0GrW97mI/izsY4R0/OkKJ1YB8KpHp8kf4wg0b2ZDGqnh8fJzR0VG2b9+ecwfhQlAFT1NTU7jdbgoLC7XPIssynZ2d6HQ61q5dm5G00WiU97znPWzevJlPfepTK0buW2+9laeffprp6Wmqqqr47Gc/SyQS99F/3/vehxCCu+66iyeeeAKr1cq9997L7t27X55Cl2g0SigU4tChQ9qc79RkWl9fn6aiWq4bIhvUVdRms2V92qulHlWQYrFYqKysXFRLogo1RF6KndNSoUZEqhHF8UEH3/5zP+NzIRqL9bz7kgbWNlQvuNedDUR454+OUGYzaN+V0xfmc2/cMG8K6tjYGOPj42zbtm3FfstU95pIJILVamXz5s0ZB0jEYjE+8IEPsHr1aj73uc+dk5V7Aby8CX7w4EFMJhNVVVVUVFRotfETJ05gNBrPOJmWK1QZaG1t7aKyyOnKb5WVlTm1iKbaK50NOJ1Ourq62LZtGxaLBW8oykcfPkE0plBg1jPlCVJsEPztOoEujVNrIoQQfPnJHg72u7AYdQQjCg0lFr5606akyGJkZASHw8G2bdvOSn98YhRWUFDA9PR02gESiqLw4Q9/mLKyMr785S+v+OSVJeLlSfD/+I//oLGxkVe/+tVaFntqagq9Xk8gEKC+vj6rCGE5oZbBUqdsLgVq+W1qagohhOYYmrq9UFfRpWiulwp1umdiXb1zwsuXn+ymImFWucMT5utv3YxVJxa0qQpHFR44PEbHuJf6EjO37q5LalwZHh5menqa1tbWs0bu7u5uFEVh/fr12nWqOQg1lP/JT35CIBCgurqab3zjG+crueHlSvCnn36a+++/n2eeeYZdu3axf/9+CgsLOXHiBPv27cPn8yUNiTuT7qRsUN1JVsJ6SPVxczgcRCIRrdauKtLUVfRsQHV92b59e9I2YsgZ4FOPdFBhNyLLEpGYwmwgyndubU2ySVZtqhwOB16vN61NVSoGBwdxuVy0traeFQIJIejp6SEajWadkBMKhfj7v/97bTTUlVdeyVe/+tUVv74l4uVJcBWxWIxnnnmGf/u3f+Ovf/0rr3vd63jzm9/M61//euD02F9JkjSyL8dAPkjuG1+uY2aCuoIMDQ3h8/k0I7+l9IMvFmq7Z7oQWQjBD58b5g8np5Gk+I96+0X1vGFj5nxAqk1VOm15f38/Ho+HLVu2nFVyq80xmb5TRVH47Gc/i8vl4rvf/S6SJDE5OXlGpdcnnniCD3/4w8RiMe68804+/vGPJ/276o0+NDRENBrl//yf/8M73pHzKLGXN8EB+vr6uPPOO7n//vvp7e3lgQce4KmnnmLt2rW86U1v4sorr0Sn02mroaIoGUPfXDE4OKiFjitpu5sI1V5p8+bNWkY+k2njciDXdk8hBO1jHpz+CHXFZloqcu/kStSWz8zMaJGWWss/W+Tu7e0lFAplbY4RQvDFL36R4eFh7r333mXZMsRiMdatW8fvfvc76uvr2bNnD/fddx+bNm3SXvPFL36Rubk57r77bqampli/fj0TExO5RqUvz26yRDQ3N/P73/8eWZaprKxk3759KIrCSy+9xIMPPsi//uu/smrVKvbv388111yD2WzG4XBoAg419M1V9KAmYJa7GyyXc6r2SuoDSl0Nl3uyirqihcPheeQOxxRmvGEKzXpspnjL6Na6pan0EocVrFmzhs7OTtxuN7Isc+jQoWW1qcqEvr6+nMj9r//6r/T19fHjH/942fIBBw8epKWlRZO+3nLLLfzqV79KIrgkSXg8Hq0dON0o4nOBs3oFqUSTZZndu3eze/duvvjFL9Le3s4DDzzAddddR3V1Nfv37+e6667DbrdrtjvhcJjy8vIkl5dEqGUwu91+1rLz6lgls9mc1l4p0bRRLfM4HA56e3uxWq1LKr+p4g5Zlufd9AMzfv7fE914glFA8K5LGrOG44s5Z3d3N0II9u7dG5+jFg5rv406mWSpNlWZ0NfXRyAQyGpdJYTgP/7jPzh27Bj333//spIrnX48tQPsrrvu4oYbbqC2thaPx8PPf/7z8yKpd+4fMacgyzKtra20trbyuc99jo6ODh588EHe9KY3UVJSwg033MD1119PSUmJZh8UCASSyJ44O+tsNVMs1l5JkiSKi4spLi5OMn946aWXMBgMOSUcs7V7CiH4ypM9+ENRSq0GwlGF//7rEBuqC2goWXqyTwjByZMnAZL2v0ajUfNAUwUpqpfbcqgCVVVettZdIQT/9V//xbPPPsuDDz647NuxdNvY1Gv57W9/y/bt2/nDH/5Ab28vb3jDG7j88svPSm9DNpw3BE+EJEls2rSJf/7nf+bTn/40PT09PPjgg9xyyy1YLBZuuOEGbrjhBsrLy5mZmaG/vx+v10skEqGpqWneYLyVwpnaK6WaP/j9fhwOh6bFVrcliTkIdbpnpnbPQERhyhvSJosa9TJSWGJsNrhkgqvRgl6vz6oW0+l0SdsStZGkq6tLs6kqLy/PeXVNTOJlI/f3v/99fv/73/Pwww+vSCUmnX489R679957+fjHP44kSbS0tNDU1ERnZ+c5d2Q9a0m25YCaUHrooYf45S9/iSzLvPGNb6SiooKenh7e9ra34fF48Hg8lJaWUllZSXFx8YqE6arL6krN6wqFQlqtPRqNauN2u7u7s7Z7CiF490+PEo4q2E16ojGF2WCUu2/cRFP54l1U1A4ttYljKd9lYqQyPT2NwWDQ9u2ZKhtq4nChDP2PfvQjHn74YX71q1+tWDkyGo2ybt06nnrqKerq6tizZw8/+9nPkqacvP/976eqqorPfOYzTE5OsnPnTo4ePZqr5uLln0VfbqjjjT71qU/x6KOPsmnTJq6++mr2799PQ0ODltSam5ujuLiYqqqqMxpzkwjVNPBMhg0uBpFIhImJCXp6etDr9VRXV2fd556c9PLFJ7oJRRUUIbhlVy037Vh8VKPmFlTjhOV6UKo2VerstFR308HBQWZnZxc0gbzvvvv46U9/yq9//esV93d7/PHH+chHPkIsFuOd73wnn/zkJ/nOd74DxDXmY2Nj3HHHHYyPjyOE4OMf//hiRgrnCZ4OU1NTvO997+MHP/gBgUCAX/ziFzz88MO43W6uvfZabrzxRpqbm5mbm2NycpLZ2dlF2RengyoD3bp161kxDYTkds+SkhJNjKKW39RIJfHzeIJRJtxBiiwGKgsWP3FF3eernW8rhVTjRoPBgBCCHTt2ZM2CP/jgg3z/+9/nscceO2sqwRVEnuCLwfT0NL/85S956KGHmJ6e1lb2DRs2aBlsp9NJQUEBVVW52yCls1daaagS23Ra9sTy2+zsLIWFhdrD60xKROr0j5KSkrNm6wRx3cLExAQ2my3rwIVHHnmEe+65h8cee+ysRFBnAXmCLxUul4tHHnmEhx56iJGREd7whjfwpje9ic2bN+P1epmcnMTpdGK1WqmqqqK8vDwtOVbCQnkhqMMBcnGaSSy/zczMLCmpBaeTeGVlZUmW1isNVc+uagiEEFqSbmZmBqvVSnt7O0ajke985zs89thjWYcUvsyQJ/hywO128+ijj/LQQw/R29vL6173Om688Ua2b9+e1C2mtoZWVFSg0+no6+vTSjVnq7apWgwvZSuQmtQyGo0YCko5NiMRReKS5tK0SrbEoXxny3QS4llpVWab7vtVP88//dM/8eSTT7Jp0yZuvfVW3vve9561a1xh5Am+3PD5fDz++OM89NBDHD9+nNe85jXs37+fPXv2EAwGmZycZHp6mnA4jNVqZevWrSvWDJOK1HbPM8XQ1Cx//7/HcfrjxgNmg54vvHEde9ecFr9Eo1FtVvbZKjNCXEQyOTm5YJvpn/70Jz796U/z+OOPEwqFePHFF3nTm9605PMupC2HeLPURz7yEc3D709/+tOSz7cA8gRfSQSDQZ588kkeeOABDh8+zOWXX85VV13FQw89xIc+9CFsNpvW5rrSnW+ql9ly7vP/57lhfvrCCCVWQ3zWmD9MtVVw13aTtsft7u6mrq5uxUYwp8PY2BgTExMLkvuZZ57h4x//OI899tiyXF8u2vLZ2VkuueQSnnjiCRobG3E4HCtp1rFiBD/3WrrzAGazmRtuuIEf//jHvPTSS7zmNa/hAx/4AJ2dnXz3u9/VzAM3btyohbGHDh1ieHiYYDC48AlyxPj4OAMDA+zYsWNZk3j+SEy7g2RZxmIyYLIWsGPHDvR6PYcPHyYYDOLz+Zibm8vk/LmsSHR/yUbu559/no997GM88sgjy/bwSdSWG41GTVueiJ/97GfcdNNNWh7ibDnxLDfyBE+B0Wjk8OHDfOc73+HZZ5/llltu4dFHH+XSSy/lH//xH+ns7KS1tZXNmzfHO7Ta23nhhRcYHBwkEAgs+bzDw8OMj48vyqgwV1y6phRJlgiEY4SiCoGIwus2lCOEYHx8nE2bNrFv3z4KCgoYGhriwIEDdHZ24nQ6V4Ts4+PjjI+Pp7WMTsShQ4f4h3/4B375y18ua04gnbZ8dHQ06TVdXV24XC6uuOIKdu3axY9+9KNlO//ZxBlJVRfax5ztOUzLhS996Uva/3/961/P61//eqLRKM888wwPPvggn/70p2ltbeXGG2/kda97HbIsJ1kXV1RUUFVVlfP8rf7+ftxuN9u3b1+RJF5rXSGfunot9z43TDiq8JadNdy4tYLDhw8nWSlXVVVpI4OdTicTExOcPHlSK7+pJodngvHxccbGxhYk99GjR7nrrrt46KGHlr1Ul4u2PBqNcujQIZ566ikCgQD79u3j4osvZt26dct6LSuNJRM8FovxwQ9+MGkfc8MNNyTtY872HKaVhF6v54orruCKK64gFotx4MABHnroIb7whS+wfv16brzxRq688koMBgNTU1OcPHmScDis6cnTiTHUds9QKLSgautMcVlLGZe1xCW16nTXlpaWtDLbxLnaavltcnKSnp6eJZffIO6eqzquZiP38ePHee9738sDDzxAS0vL4j5oDshFW15fX095eTk2mw2bzcarXvUqjh49+soheC49sr/61a+4/fbbkSSJiy++mNnZWcbHx89qImcloNPpuPTSS7n00ktRFIVDhw7x4IMP8tWvfpWmpiZuuOEGrrnmGiwWizbdI7XzDaCzsxNJkrK2QS43gsEgR44cYd26dTnVkTN1vw0ODmI0GrVy4kJJx8nJSYaHh7V9fyZ0dnbyrne9i/vuu4/169cv+vPlgj179tDd3U1/fz91dXXcf//9/OxnP0t6zf79+7nrrruIRqOEw2Gef/55/uEf/mFFrmclsWSC59Ijm2mv83IneCJkWWbPnj3s2bOHL33pS7S1tWk97TU1Ndxwww1cd911FBQUaJ1vPp8PIQRFRUVZrYeWG2qDzIYNG5Y0BCG1+y1xEol8yp01nd2Ww+HQBiFkI3d3dzd33HEHP/nJT5IaOZYber2ee+65h6uuukrTlm/evDlJW75x40auvvpqzbHmzjvvZMuWLSt2TSuFJRM8l31MLq+5kCDLMtu2bWPbtm18/vOf58SJE0k97fv37+e1r30tjzzyCG9605sQQvD8889TWlpKVVVV2qkdywVV8rpx48Zlk3eq4evq1au1EUqqyaFKdp/Px+Dg4IKDEAYGBrj99tv54Q9/SGtr67JcXzZce+21XHvttUl/9773vS/pzx/96Ef56Ec/uuLXspJYMsFz3ccs9JoLFWrovXnzZv75n/+Z7u5ufvrTn3L55ZezdetWqqqqeOMb38jGjRtxuVyMjo7S0dGRsXnkTODz+Th27NiKDldMHKGkNpC0t7fj8/moq6sjEAig1+vTPsCGh4e57bbb+N73vveySMK+nLDkOyhxHxMOh7n//vu54YYbkl5zww038KMf/QghBAcOHKCoqOiCCs9zhSRJrFu3jq6uLr71rW/x3//934TDYW6//Xauu+46/vd//5fi4mL27t1LRUUFk5OTPP/885w4cYLp6WkURVnyub1eL8eOHWPLli1nzV3EaDRiMMQnoezbt4/i4mIGBwc5cOAAJ0+exOVyadHd2NgYt9xyC/fcc885N0e4EHFGSraFemQzzGHKekELld5++tOfcvfddwNgt9v59re/zbZt2xb+pOcBwuFwUjJKCMHo6CgPPfQQDz/8MNFolOuvv579+/fT2NioZa9V2+KqqqpFlarUvvWzOXgB0AY5ptb01fKbw+Hgueee47e//S39/f187Wtf48orrzxr13ce4pUhVc1FQvjss8+yceNGSkpK+M1vfsNnPvOZl23pLRFCCCYnJ3n44Yd5+OGH8Xg8XHfddezfv581a9YkzUmz2+1aqSpTucntdnP8+HFaW1vPWt86wMzMDL29vWzfvj1rZn1sbIx3vOMdVFRU0Nvby/ve9z7e//73n7XrPM/wyiD4c889x2c+8xl++9vfAqcFJ5/4xCfSvt7lcrFly5Z5KqQLAVNTU1pP+8zMDNdccw033HADGzZsSOoUs1gsWpurmsRSO9HUwYNnCzMzM/T09GSdCa6+7s1vfjOf+cxnuPbaa7XZb2caZeTSQALwwgsvcPHFF/Pzn/+ct7zlLWd0zmXCy98XPRfkUnpLxPe//32uueaas3FpZx0VFRW8+93v5t3vfjdOp5NHHnmEz372s4yMjHDVVVdx4403smfPHgKBgGZEYTKZNIvp7du3n7WRSRDvgMuF3C6Xi7e+9a186lOf0rLY6mzwM0Euwiv1dR/72Me46qqrzuh8LxecV1r0xZTV/vjHP/L9739f249fyCgtLeWOO+7g17/+NU8//TRbt27lq1/9Kpdddhl33303s7Oz7Nmzh1AoxOjoKJIk0dHRwcjICOFweMWvT21vXSgsd7vd3HzzzXz0ox+dl5A9U+TSQALxgZhvfvObX7bNI4vFebWC51pWO3bsGHfeeSe/+c1vVsTR9HxGUVERb3vb23jb296G1+vl8ccf55577uHQoUPEYjG+/vWvc9lllxEOh5mcnNREKGqb63JbTblcLrq6uhbsgPN6vdx8883cddddvPnNb17Wa4DchVe/+MUv+MMf/sALL7yw7NdwPuK8InguEsKhoSFuuukmfvzjH7/sdMHLDbvdzs0330xJSQn9/f3cddddPPjgg3zyk5/k8ssv58Ybb2Tfvn1Eo1EcDgdtbW0AWjPMmQ5jnJ2d5eTJk2zfvj0ruX0+H7fccgt33nknt9566xmdMxNyif4+8pGPcPfdd5+VEcfnC84rguciIfzc5z7HzMwMH/jAB7T3vPjii+fyss851qxZo0Uzt99+O6FQiKeeeor777+ff/qnf2Lfvn3ceOONXHbZZSiKgsPh4Pjx4yiKoinOFpuMm52dpbOzk+3bt2d9UAQCAW677TZuu+02br/99jP9qBmRS/T34osvcssttwDxUt7jjz+OXq/nxhtvXLHrOucQQmT774LAb37zG7Fu3TqxZs0a8aUvfSnj6w4ePChkWRYPPPDAWby6lUU4HBZPPvmkeM973iM2b94s3v72t4uHH35YOJ1O4XK5RFdXl3jmmWfEH//4R9HW1iYcDofw+XxZ/xsbGxNPPfWUmJmZyfo6p9Mprr76avGtb31LKIqyop8zEomIpqYm0dfXJ0KhkGhtbRXt7e0ZX//2t7/9fPqdF+Lhkv87r1bwlcArPbtqMBh4wxvewBve8IZ5Pe3btm1j//79vO51r0Ov1zM9PU13dzfBYDCpzTUx1FVLcAvNWw+Hw7z97W/n6quv5v3vf/+K9yDkEv29EnFe1cFXArnW1r/+9a9jMBh44YUXuP7668+X+uiKIRaL8dxzz/HQQw/x+9//ng0bNmg97SaTienpaRwOB36/X5sYCmjkzlaCi0QivPOd7+Siiy7iox/96AXdYLRMeGXUwVcC+exqeuh0Oi677DJtX/7iiy/y4IMP8pWvfIXm5mb279/P1Vdfjc1mY2Zmhr6+PpxOJ9XV1YRCIcxmc1riRqNR3vOe97Bjx448uc8DXPAETxeh5LOryZBlmb1797J3716+/OUvc+zYMR544AG++c1vUltby549e3juuef40Y9+RCAQmNf5VlJSgiRJ2nZo3bp1fPKTn8yT+zxAPkQHmpqatAfB9PQ0VquV7373uxd2djUHCCH4xS9+wQc/+EGam5ux2+3s37+f66+/ntLSUlwuF5OTk0xOTnLvvfcSjUZpaWnhK1/5ylkbEHGBIG+bvFTk0tba39/PwMAAAwMDvOUtb+E///M/X/Hkhnikc+DAAZ5++mmeeeYZvvnNb+Jyubj55pvZv38/Dz/8MGVlZVx66aWYzWZGRkZ48sknl8Uk4YknnmD9+vW0tLTw5S9/ed6///SnP6W1tZXW1lYuueQSjh49esbnvCCxQJr9gsBjjz0m1q5dK5qbm8UXvvAFIYQQ3/72t8W3v/3tea9dTPkkl/LbH//4R7Ft2zaxadMm8apXvWrpH+I8gqIooqenR9x9993ikksuEatWrRK33367iMViIhaLid7e3jM6fjQaFc3NzaK3t1creR0/fjzpNX/961+F0+kUQgjx+OOPi717957ROc8xVqxM9oog+Eogl5vQ5XKJjRs3isHBQSGEEJOTk+fiUlcUiqKIgwcPilAotGzHfPbZZ8WVV16p/fmLX/yi+OIXv5jx9U6nU9TW1i7b+c8BVozgF3yIvlJ4JU3HyAZJktizZ8+yjnLKZTBBIi7krsIzRZ7gS8QraTrG2YbIdxUuGy74MtlKIZeb8EKZjnG2ke8qXD7kV/AlIldXWVUsUl5erk3HyCM7cql85LsKc8QCm/Q8MiCX5oYTJ06I1772tSISiQifzyc2b94s2traztEVv7ywUOXjXe96lyguLhbbtm0T27ZtE7t27TqXl3umyGfRz0fkUn77yle+IjZu3Cg2b94svva1r+V03IXKb7Ozs+L6668Xra2tYtOmTeIHP/jBsnyePM4ZVozgF7yS7eWGXJxlv/jFLzI3N8fdd9/N1NQU69evZ2JiYlkz2XmcVeSVbK8U5FJ+kyQJj8eDEPFhgKWlpYue9JnHKwN5gp9nyKX8dtddd9HR0UFtbS1bt27lG9/4Rl77nUda5O+K8wzptkyp5bff/va3bN++nbGxMY4cOcJdd92F2+0+W5eYx8sIeYKfZ8il/Hbvvfdy0003IUkSLS0tNDU10dnZebYvNY+XAfIEP8+QSw24sbGRp556CoDJyUlOnjxJc3PzubjcnLFQd5gQgr//+7+npaWF1tZWXnrppXNwlRceFsqi53EOIEnStcDXAR3wAyHE/5Mk6X0AQojvSJJUC/wQqCGegf2yEOIn5+hyF4QkSTqgC3gDMAK8ANwqhDiR8JprgQ8B1wIXAd8QQlx0Di73gkKe4K8wSJL0A+B6wCGE2JLm3yXgG8SJ5gfuEEKc0XIqSdI+4DNCiKtO/fkTAEKILyW85r+Ap4UQ953680ngCiHE+Jmc+5WOfIj+ysMPgauz/Ps1wNpT/70H+PYynLMOGE7488ipv1vsa/JYJPIEf4VBCPFnwJnlJfuBH51SWB0AiiVJqjnD06YTcqSGjrm8Jo9FIk/wPFKxEivpCNCQ8Od6YGwJr8ljkcgTPI9UrMRK+gKwVpKkJkmSjMAtwCMpr3kEuF2K42JgLr//PnPk9Y15pGLZV1IhRFSSpLuA33K6MnA8sTIAPE48sddDPLn3jjM5Zx5x5LPor0BIkrQaeDRDFv064C5Ol6u+KYTYe3avMI/lQn4Ff4VBkqT7gCuAckmSRoB/AQyQX0kvRORX8DzyuICRT7LlkccFjDzB88jjAkae4HnkcQEjT/A88riAkSd4HnlcwMgTPI88LmDkCZ5HHhcw8gTPI48LGP8/H18apNyom+kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X_random[:,0], X_random[:,1], X_random[:,2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### demean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def demean(X):\n",
    "    return X - np.mean(X, axis=0)\n",
    "\n",
    "X = demean(X_random)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X[:,0], X[:,1], X[:,2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(w, X):\n",
    "    return np.sum((X.dot(w)**2)) / len(X)\n",
    "\n",
    "def df(w, X):\n",
    "    return X.T.dot(X.dot(w)) * 2. / len(X)\n",
    "\n",
    "def direction(w):\n",
    "    return w / np.linalg.norm(w)\n",
    "\n",
    "def first_component(X, initial_w, eta, n_iters = 1e4, epsilon=1e-8):\n",
    "    \n",
    "    w = direction(initial_w) \n",
    "    cur_iter = 0\n",
    "\n",
    "    while cur_iter < n_iters:\n",
    "        gradient = df(w, X)\n",
    "        last_w = w\n",
    "        w = w + eta * gradient\n",
    "        w = direction(w) \n",
    "        if(abs(f(w, X) - f(last_w, X)) < epsilon):\n",
    "            break\n",
    "            \n",
    "        cur_iter += 1\n",
    "\n",
    "    return w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.84785927,  0.33792667, -0.4085832 ])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_w = np.random.random(X.shape[1])\n",
    "eta = 0.01\n",
    "w1 = first_component(X, initial_w, eta) \n",
    "w1 # 求出第一主成分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 将原来的所有样本点X去除在第一主成分上的分量，得到X2\n",
    "X2 = np.empty(X.shape)\n",
    "for i in range(len(X)):\n",
    "    X2[i] = X[i] - X[i].dot(w1) * w1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PTYfo4+PjtLa2smXLFsxms37xnD9/nmAwSGFh4aJOWC2yGhkLRnmufYSYEGyvK2J99UTks3N5MdVFZhzjEQosRtZUzHwjWlll55/ebgcmvoPXXnuNaDQ6RbFWWlqa1QGS2Y6QZqrhd3Z2EggEaG1tJT8/n87OznnV0CVJugn4BmAA/kcI8eUZHrcLeBV4rxDikVSe+6Iieqq18ZkaYKLRKK2trZhMJnbv3q2HUuk6u2qP13rfg8Egu3fvTnqBpppJV1WVrq4ugsEge/bsQZIkotHolDqwqqqMj4/jdrvp7+/XlWtag0s2En6DYyF+fKAfs0HCIEv84sgg79kOGybJXmfPo86ex3goxv+81MMZh59Sm5k/3lVDQ1nyXUtTfy1fvpzly5ejqmrGzSeTYbGPQvHf3YEDB1ixYgWnT5/mS1/6EufOnePDH/4w73nPe3jrW9+ayvMZgG8DNwB9wEFJkvYLIU4ledxXgF+ns96Lguipjj/SkEykog0yXLlyJcuWLZvyu5luDDNBkiSCwSDt7e1UVlayfv36GdeTSuiuSV6Lioowm80Yjcak65FlmeLiYoqLi6co17TkkMlk0gUgmRq7dGrIhyRBaf6F6OFIz5hOdA0/eq2Psw4f5QUWxkNRvv1CN5+/uZHiFM7hWuJOUwImvq/4OXIzedClgqXoddegyY137drFfffdx89//nM++tGP6s1KKWA3cE4IcX7y+R4C9gKnEh73CWAfsCud9S050dMZf6QhPnTXlENDQ0M0NzeTn58/7fHpylRDoRDDw8M0NTUtWKbqcrloa2tj48aNyLJMb29vyutIFHiEQiHcbrdu2VRQUKATf75dX0ZZQlUvrF8VYEggSySm0jbsY1mRBX9EYdAbZjQY5fn2EfY2V095bCqRU+L70ubI9fX1MT4+js1m04mfThurqqpLomdPTAL6fD4KCwvZvXt3Ok9TC8RfHH3AZfEPkCSpFng7cC2vJ6JroWpbWxtNTU0pf6EacZMNMpzt8XNB0457vV4aGxvnJPlszy2E4Pz584yMjOhGkl6vd0GlF6vVSk1NjT52KVHAooX56RhUbKkp5GD3GINjIQyyhKIK9qya+r6NBgmzUWY0GKNlwIuiCiKK4JGjQywvzWNb/UTe4oWzIzz4Wh+hmMoKc5QtWxWsprnXkThHThsnldjGWlpaOmveYql29Az1uSe7+BMvlq8DnxFCKOlGPUtC9PhQXZZl3bInVRgMBnw+H52dnbP2lmtIheiadrykpISampqUiZJsR48Xt+zcuVO/+DJZR08mYElmUFFaWjrra5bmm/nQFXUc7/cSUwSbagqpKZ6aJZcliffvqOGrv+3AH1GwGg3UFFuoKDTz9Ckn2+qLOTPk47t/6KbIasSeZ+LEsI+fHOjnzjctT/t9xY+T0tpY3W43ra2t+g0tWTfb65zofUB93L/rgIGEx+wEHprkSjlwiyRJMSHEY3M9+aITPbE2PtN5dba/HxkZwev1smvXrpTKGHMRPVE73tnZOS9nV7jQMbdq1Sqqq6tnfWwmkdj8ER8Ou91uPbRPZkBZmm/mmrXlsz7/zhV2bt1cyVOnnFQVWrDbTPhCF0YknR4aRwCWyR280AxHer0Lfl/xbawNDQ26I412hJEkSd/t45tWFhOJRNcMP9PEQWCNJEkrgX7gfcAfxT9ACLFS+/+SJP0QeDwVksMiEz3R4kn7L9WLXxtkCFBfX59yrXK28DqZdjydM318Rl8Ty2hlvWRYrK6p+HC4p6dHH2GkGVBq5a6SkhLGI4Jhb5h8i4E6u3XG6OrGDRUc6hkjpgpGA1GCUYX376wBoDjPhBAXuvAiCpTYMl9GS3SkiUajeDwehoeHcTgcjI6O4vf7M5qwnAuJkUQgEKCuri6t5xBCxCRJuouJbLoB+L4QolWSpL+c/P13F7LGRSF6KrXxuaDtumvWrNHbWlNFsiy9dtPIz8+fph1PtwlGE8tEIpE5xTJLAUmS9BpwfLnL7Xbz0snz/LorhtFsxmy28Ja1FbytqTopQZYVW/n0Dat55oyLUFThilUlbK2bOJ+/aXUpv2sfocPpn/xbiT+/Ir2LfT4wmUxTjClKSkp0sZHP55tiNZ2tbrVkofs8dnSEEE8CTyb8LCnBhRAfTOe5s070hXqqxye1tF3X5XKlFe4n7tBzacfTKceFw2G8Xi+VlZVs2LBhzven3UAysdMEIgpHe8fwBKIsK7bQVFuEyZCabFc74/6sXaVumUBWIgQCQfYf6sAaGGJjfUXSrHd9SR5/fkX9tOe0GGX+381rON7vJRxTCQyco7Ei/Yt9IdA6DQsLC/WEpd/vx+12Z9VKOxnRLyZ3Gcgi0dOtjSeDliArLi6ektRKt1ymEVcIQU9PD4ODg7Nqx2VZTqmTbmRkhNOnT2O1WmloaJjz8Zk8o0cVld+edjIWilFgMXCib5zxkMLVa8tSfo6JEDxCWb4Ja56N/Px8FHOYimXlQGhK1lsLl2cjh9kos2uFHYCD7sVXbiWG0Fptu6CgQI9kvF4vbreb3t5ehBAZaUjK1I6eTWSF6KlaPCX+Tfzj4gcZavVWDamKWjRoRD9+/Dgmk4ldu3bN+qXO1UknhKCrqwuHw8H27ds5fvx4SuvIJNHHgjHckzs5QJ5JpnMkwBWxEizG6bt64usKIXjmjItOd4hTQ36K84ysr5o40y6vKKIsv5za2lrCUYVQwKfPWtO62mazo1oq9VY6MlWY7jirNe6ka6V9sdtIQRaIPp9QXduhtbO0Nshwppnj6e7ofr8fr9fL8uXLqampmfPxs7W1xmIxWlpasFqt7Nq1a16iFli4OYE8+bHGFBV5UhYqSxd+rmHIG+LnJzyMhQTr61Rub6qiOM9EhyvA79pH2LW8mDPDPoa9YdqG/Xzh1rWU5ZvpcPr57os9jAWjVBdZ+aurlrNq1SpisRgejweHw8HZs2d1RVd88msp3GVguvHEXJipcSddK+1Eol9sxpCQQaLHh+rpJty0HToajSYdZDjT41OBph3Py8tLieQw841EK50la7NNBRoJIpEIJ06cIBAITOluS0flZTMbGAvGeLVrFJNBoq7Iwk2bKqec0f3hGD96rZ9gRKWiwMTAWIiHjw7y4Svq8QSiSNLE82yvLyYcU/CHFdZVFeALx/iP57swSBLVhRY8gQj/8XwXX7xtHUajcYqUM3HAYmFhIXa7fUl29YWW1xIbd1K10lYUZcqR5g0fus93UqnBYMDhcNDd3c369ev1WvBMSGVH17Tjmm3UgQMHUl5PstB9cHCQzs5OtmzZMu+7tSZkOXToEKtWraK4uJhgMIjb7ebMmTNEo9GUu9sO94xhM8nsXF6EL6wQjalUFV24+HzhGN9/uZfXujyYhEJjmURjTREDYyECEYVS20Q5LKYKjLLEWChGQ+lEzmLYGyaiqFQWTDxfqc2MwxdmLBilLH9qZ1peXp5+E9WqIS6Xi2AwyMGDB+fVrTdfpLujz4ZE0Yr23jwezxQr7ZKSEqLR6BRiay2wFxMyRnRNsZSuJ5qqqvj9fvr7+2ccZJiIuXZ0TTteV1dHXV1d2jee+NBdU7CFQqFZS2epYHh4GL/fzxVXXIHNZiMSiUxJFiV2t80mYun1BCkrMGOePI8PTfafL5vsanuq1cFIIILNZEBWVc6OhLEXRTDKMmajzKpyGzeuL+fZNheSJFGWb+Zd2yailEKrETXuJhCOqUhI5Jvn9sQrKioiLy+PsbExmpqaprwfo9Gov59sjIteqPHEbNDem+Y/Fz9KamhoSG/icjgchMPhtDX4c0lUJUn6Y+Azk//0AR8TQqSWHGKJe901VZfBYGDdunUp669nu6FowxhmcnhNBVrEoM1Er6iomFXBNhe0qaxaXbegoCDp+hO72xJFLIWFhZSVlU0kwvJMOH0RzMaJ6ENRL9hAAXS5g9SX5KGograBMKGYYHAsxJ9fUa+H9zdsqOCylSWEowp2m0n/eWWhhdu3VLL/xDCSLIGAD1xeN2vfuhCC/S3DPHRogKiisq1UoXmrPK1bz+1209PTM2VcdLrHltnWsFi9CvGNO7FYjIqKChRF4Wtf+xp9fX3ceuut3HDDDXzqU5+a87pJUaLaCbxFCOGRJOlm4AESRC+zYcmIPjw8zLlz59i4cSNDQ0NpRQLJkmXxO2/8MIb5QJZlQqEQhw8fTukoMRsikQjHjx+ntLSUrVu3pnWESBSxjI+PMzIyQn9/P3khBc+YmTFfHiazmbWVBdSXXGgIqSgw4wlEaazIxxgL4giovH9XLVtqp978iqxGsE6/DG7dXMWWmiLcgQjVRZak7q/xePG8h/9+qXcigpDguZ4oa48O8u7tF/IiFotlinGDVuPWzCniw/yLYapqqojFYpjNZgoKCviP//gPjh07xgMPPMDBgwdT3RzmlKgKIV6Oe/yrTPTCp4xF/zTjzRy0UN3pdKatF4+HFhnMpR1PBUIIBgYGGBsbY8+ePQvaaTTLqDVr1lBZWbmgTHt86KiNXV7tHKFrcISA30NZaIyhwbDe5HLrpkp+dnCAwbGJ3fyqhiJ2Li+e+4XisLw0j+WlqXWTvdbpQZYmaumqCmYDvNw5OoXoie8n8dgS38Mebz6ZTqlrKZDMAVYz3UgRc0pUE/Bh4Kl01phRos9FsPhBhvGETLcuHg+n00l7e3tKI47nQiwW4+TJk7pQYiEk1/ret27dOmMGdqFGhvU11dTXXMgQj4yMTOllf8eGEmJGG54RmRp76n50MVXwVKuDE/1eygvMvHPrMt00MhlGA1FiqohzfRUoKtjzUr+8EnvYNWPGgYEBvF4vNpttSqnrYkKip/s8vtdUJKoTD5Ska5gg+pXpvMCi7eiz+a7NJ4knhKC9vV1Xsc11vtfC/Zl2Bp/Px4kTJ2hoaKCkpITTp0+ntR4NsyXvspko0jLE2oSSsbExHE4X/c5uJDWKOVZEfn5+Skmwnx7o57dnnBRYjJx1+Dk16OO+29dRYJl+uTzXPsI3nuskJgQuX4SIomIxSJiNEh+8fHqrbKqIN2bUNOput1vv1stGK+t8EU/0YDA4nxtRKhJVJElqAv4HuFkIkZrH+CSyTvT4QYYz+a7JskwsFkvy18kRDocJBALIssyOHTvSaspJRnQtgaeVztKxcI5H/Hl8oUeIhUCWZVRzPk/2eRjxFzE+Ps4eRUGSevSE4EzONIoqeK59hMpCCwZZotBqxDkeoW3Yz46E0N/tj/CN5zoxG2QKjDJmWWY8HOXPdlVTK3tZkWLYPxfiNerajSyxlVVLii2FJj3+NefpADunRFWSpOXAL4E/FUK0p/sCWQ3dZxtkOGURk/7oqUBTsVksFhobG1NeW7Lau6qqtLe3EwgEpk1TTTfC0IQya9eu1ZtJlhKPHB3EG4qxrMiCWQ3y6rDKm7auYmOxFZ/Px8jICKdOndLHEmlJsIk+CK2NdeL7EohpHXcATl8ECfQSn81sQBWC5pp8hNeftfeW2MqqSVX7+/s5dOgQFotFv5EtloW29hrzaX9NUaL6/4Ay4DuTrxUTQuxM9TWytqPPNcgwHqk0wCSq2I4ePZrW3TvxNcLhMMePH6esrIxt27ZNuRjSbbGNRCKcOnVqziGLC4E/HOPVzlFGJocY7l5h1wkGF2reMGl57QlRVThxnDHKEjFF0O7wU1Vo0Z1pGhoaphg1njt3DovFwptqjfyuK4TNbCSiqNQUW1lffeHiVVTBj17tZX+Lgz5PkNJ8E5WFFkJRFYMsUZpnxD2+eNGMyWSivLycnp4edu7cqTchxXe0acTPtoV2tiSqQog7gTvnu66MEz3ZNJO5YDAYZg3dNe14QUGBrmLTzvXzIbrW3ZRMMJP42NmgqipnzpxBURR27NiR1kWUzi4TVVR+1TLMWGBCqXa014s3FOOWTZX0eoI8emyIsVCM+hIrb2+upjjPRE2xhRFfhBKbiU53mPOeKLHDg7xyfpS/uHK5nlxL7PcOBoOUjYxgVoL8rsuLwMjKIuuE7Zck8ZMDfTzd6qR/LESN3UploYUhbxiYCPM/e+Nq8kzyoh9b4q+FvLw8amtr9Y42Lcw/efJk1i20L8b2V8gw0f1+P4cPH05pkGE8ZkvGjY6O0traqpeoNGiKtHQmqiqKQnd3N4ODg2zfvn1GI4JUhCpaRFBRUYHNZstqe6fbH8Xtj+pTUoQQHOoepc5u5elTDqwmA7V2K0PeMPuODfGhK+p559Zl/PDVPs46A3S4o6wss7Cy3IbLF+YXhwf4+Fsakr5WXl4edXV1+M7H8DGCQVJ58oyHo90jmA0S7WMSYyGVsCLoHw2xssyGLMG2+iLuvbGRfIuRsbGxJSV6PCRJmtVCe6HdeonXiZYDudiQUaIbDIZ59YInK6/NpR2fT0mura1tTsdYmHu31c7jWkTgcDjSTt5p4pZUbJoNsoQ6WYN3+SIc7h3DH1H52aF+xoIxXQNeWWhhYCxEMKpQVWThnmtX8uwZJ+P+APVFEzu43WamxxOc9fW8oRgvnHVTUWhGliSEsOL0RRj3xyjNk/CHw4SFIBJVGA+EUZFoKLPxSqdnoptOKNyw3MC6tD6RhSHV6G4mC22tWy9dC+3E170YJaqQYaLn5eXNq6MpkbRaPdtsNs9IynTO0X6/n5GREerr61mzZk3a64tHX18fvb29U24+6Z7pNZWelt0vKSmhrKxsRn13ab6JNRX5nBn2cazXiyTBpmUF2PNMtA+7GAtEKbaZCEUVLAYZ82Qrq8Uo01hZgEGeOFcDePwRlpdNRDJRRcUxHsFskCgvMOs3ON0FZ/L1JUlCZkKsZDSZqS01ct4VIKoI/BGFEgt4hvp48BUV2SAjBJzoV1nVMM7GZYsj7phvtn0uC+14b71kUdslSfT5hmvxRNekoA0NDbPKSlPd0YeHh+no6JjScz0fqKrK6dOnicViU8Y9QXqGEoqicPDgQVauXElJSQmqqjI6Oqrru61Wq97Prh0tZEliVbmN1sFxfBGFjdUFLC+ZsHiqKbYw4J1QpCFJvGtbNf6Igi8co8RmYk2FjTevsPH0WR99XT6USbFK10iA/36pl0FvCCHgzY2lfPDyOmRJoshqZFt9EUd6veSZZEJRldoSK1eV2/j1aScGWaI830yJzcSf7q7lilUl/M2+UxgMfoySQFEVgjH4xasd/N0NjYti0piJsloyC+3Ebj1tt9cmysRisYveXQYugkktcIG02m45m4uqhrl20Xghya5duzh//vy8u+/C4TDHjh2jqqqKFStWTLtoUyW60+kkGAxy+eWXU1hYSCQSmRJKJutwKykpIWgo4KlzPux5ZqqLzLQ5/JTYjNjMRlZV5HPrpspJBdqEocT3Xz47Yb1slPnwnnrWlVv4RYsXkMgzyRzsGeMjPztBnT2PykIzqip4vn2EzcsK2d0wUWL762tX8ciRAU4P+6kvsfK+HTUUWo2sqczn1KCPZcUW3ralCtukos1gmJhbbzZNfJdhNYrJIE8R5GQz850Ns4tk3Xqa0442USbxOvX7/WmXV1NQrkmTv78FCAAfFEIcSec1Lgqiw8RObrFY2LVrV8qZ+pmIq3nNlZaWsn37dl1CO58mGC0ZOJu4Za6bjmY95XK5sNlsFBUVJV1LYoebJlt9/Hg/oy4fss1IY1EeSkymbdjP1rpi3r1tmS5mcfkiPHxkkFKbCYtRZjwU44ev9rGuMMZoSKEkf+LMbTFKDHojrCjVjh4Ssgz9YyF9LRajzB/vnq6buKqxlHyzgVBMJRBRdKL/ya4avvDkWfwRBUVRsBhl/mhPI6vKbVMEOS0tLVOOK0VFRRlpcEnWb55pmM3maRNlNDeaAwcOcO7cOc6dO5eSf6CGyWt4LuXazcCayf8uA/6TNJRrcBEQXWuqkWWZLVu2pD2WKREaMRMbV9IdtAjo45dny9DD7Du6oiicPHkSk8nEjh07ePXVV1N+fU222lAPbryUWiUCgQDlxgAV1hjXVlnIU/zEYiaMRiOjwSgS6J5xhVYjA94Q+kc62QOjCDAZJHzhGGX5JlRVoKpQWzx7b38gonDPI630eiZuCBaTzL+/YyOrym28ubGML+818MRJB0o0zPUrLKwqt+mfT7wgR7OjGhoaor29XbdsKisrm7clcza16MmgdetpSb3Vq1cTi8X4xS9+wf33388DDzzAd7/7XTZt2jTr80yqGecarrgXeFBMXGSvSpJklyRpmRBiMNX1LukZPV47rolJUkXiji4m56IPDAwkzdKnkzBTVVW3EZrLSBJmJnooFOLYsWN6Z+B80VxbxMmBcZwBFbBQUWnlPduXYVVDjIyM0NnZidFoxGCzE4vFCMVMWI0y3lCMQouR7cuMrLCb6RmLIUsThC20GkEIhsfDSEhcs7aMnSsmWlyd42EO9UyUyC5rsOuDGB4/OUzXSJAiqwFJkvCFFL7z+y7+9R0bAdi1ws6uFXYcDsesU0Tj7ahmEuRoCbBUk7tLPY5JlmX27NlDQ0MD//Iv/8L69etTEkX19/fD3Mq1ZOq2WmBpiA6pnVe1RpNwODxv7Xg8cRVFobW1FVmWZyRmqkQPhUIcP35cLxWm2kef+J61ppy5VHVD3jBHesaIKiprqwp0J9Z42G0m/mR3LeecAVoGxuhwBvnvl3rZ3WDnhvWraZQlwuEwIyMjvKlylKfODWEwmijOt/Kxt6xGDoxw31vreKg1wNOnHZTlm1hZbsMfUdlaW8wf76rRs+69niCfeewM/rACCH520MRHr1xO10iAA12jqFy4oZuNEk5fZNp7Sue8PJMgZ2RkhO7u7qQJsGRYaqJriJ9ymwpm4EriD1NWt82ERQ/dNe14VVVVSgMPZoK2owcCAY4fP059ff2sY3BSCd01cm7YsIG2traU15LYG68lFWcK+bUvd8Qf4YmTw+SZDBgMEi+cHUGSYH3V9ERkcZ4Jm1mmwxmkusiCLEm81OGhwGLkytUTNd+amhreWVPDNTvCdA17MEbHefgPLRx3RLFZTGxfWc7KMhuVk403+RZBy4CX8oIG/Xt46NAAwahCWcHEzbfXHeTex86QbzEQjqqMh2Pkm2SMBolgVOX6JBr3hSTGEmepawmw3t7eWevcFwvR03WAnbxm51KupaRumw2LSnSthJQJ7bgsy/oFkEz6muzxMw1liA/7NXJq5E0lwaNFMVqkoin14v82ElPxhqL4IhduxP2jE2fdokndthCCE31eVpfbkk5c6XQFsZoM+u/seSbOOvxcufrC7vFql4efHxxAUQX+cIyYyKOkYKJn/amTDhRVxSrCmC1mhGTEbJQJx1Ri6oQd1ZlhH8GoQoEy8TqjwRgWk6yH78qoYCwUw2KUuWpNKR9JMi01kxnwxARYYp1bM6eIxWJLRvT440W65bVdu3bBHMo1YD9w1+T5/TJgLJ3zOSxS6K6qqj53fCbt+Fx68XgIIXA4HIyPj3P55ZenVK6ZKXTX5qYBU8L+eK/5uSBJEpFIhMOHD1NWVjYtUvEGo/yuzUUwGqNjKEZJt4cdy+0YZYnJPhZCUYWD3aNEFRj2Rbh2bRmbEppNivKMRGIXopJAVGF1XC5iYCzET17rp8RmIqqoHOgeRRWCqnwDjeV5VBqsRFWBN6ageiOEoz5qC2Te898HQJL1m9BoMMqIL4LFZCAcUxFCEIqqWE0y+WYDf3Hlcm5vqsaQTNJGdkpdML3OHd/O6nQ6dcItpmpNUZQpkUW6DrCTa55LufYkE6W1c0yU1/483XVmfUfXDBbLyspm1Y5rofhcRNc80Y1GI9XV1SnXZJMRXUuW1dTUTJPRzjWtJR6xWIwzZ86wfv36Kf34Gg52e4ipKpWFVtxWmdMDXurseTSU2Tg5OM7gWJgzQ+OMBmNcsaoEq1Hmt6ddVBSYqSycuIjGglHOu/x0jgQ5PxJgeUkeZQVmrl5zoeQ37J2Q+soSHOv3IgOKEPgiKu2uEJVFeVQUmOl2B7FZLVy1rpJn2kaw500YR3oCArtVojLfyOB4lIgSw2Y2EI4p9HqCVBVaMBllti+3z0hyyB7RExHfg5CXl6dvFJpqraioiLKysqyaUySG7pFIJO0+gRSUawL4+ELWmVWia2OVUjFY1Ig+2xcSr/mWZRmn05nyWhKFM5qufaZjRKqa9OHhYVwu1zTRTTxGgzHdnUWWZWQZglGV0jwjb9tSTbc7QI87yKbqQgo0o0YJPIEolYUWoorKj17tY8QfoammkL7REDazgY++afkU1xe7zYQqYDwUIxZTMZtkoiFBTBGMBmNElRBnhnwAqEJwzumnrMCMzWpF9qsYjVEiQqLSIjE8DmYZqvMlRsNGxsMKBVYjf//WxjkNJRbTjVWDqqpYrVaqqqqora2dZk4B6Gf7oqKijN2Iks17uxj97bIWuidOQJ0LszXACCHo6+ujr69PL515PJ60By2qqqqLZYaGhmZdWypNMB0dHYyNjbFs2bJZ3+OyQgvdngCVhVZiqoo/rCBLEyIVm9nAhupCNi0rwBuakOqqQqCqgnzLxE4x4o/i8kdYNunEuq6qgAFvKM6jbQINpXm8dWM5jx2fkK2qAvLMMjFFJd8sozKhWTebJvrRvcEoo4EoywotFFuNuHwRjCYDRpMZpCiFeSaMRpliEcUg4N2roVL2EQqZZ32/SzGSKZFwycwp3G43AwMDnDlzBpvNprcaL8QbML4FdqFjtrKJjBM9Eolw7NixKdrxVDAT0bUztBBiSoJrPoMWtblpWhluroF8c81fs9lsbN++nY6Ojlm/4O0r7ARjKv2eAC0uhTpjmMdbhig3hLh+Uw2FBflcv76CXx4bYmgsjCoEO1cU6w0sRllCUQWKqmKQ5QmBymTTSzwkSWJvUzX2PCP3Pd1BKKpgMEggVKxGA0FFIE2+ZQkwGmRK8kx4AhNJyjq7FbNRJqbCDevLOTk4znhEYJBM7FxVyI076hnzuPWefy0RZrfbp3yWGtE7RwL0ekKsLMubYkWdDcyV3zGZTFM86JJZTZeVlaU9USZZHmepLMRmQ8aJ3tfXR319/Yxh7ExIRlzNNXamM3Q6RI9GozgcDtauXZtS88pM/QBaOW/FihW66GauMN9qMnDtunJeOjfCmTwDa8os9PX1cYY8zLGzVJqjFBcXc2tjCcJcQJ7FqI8+CkUVnm1z0eMOcrzfy8rSPAqsJq5eUzYlbBdC4AlEEUCeycDyUitmg0xEEaiREGFVosJk4tSQD1VVUVRBgWXCKKIoz0RUFawut015zpMD45wZ9lFiM3FVYykmg0xx4QV7Zo/HozvTxHe3CSF4+ISbHx09h8kgEVUEf//WRt6xtTrVryttpFNeS2Y1nWyiTFlZ2ZyCnPgz+lKV+FJBxom+atWqeYlHEomu2TjPVDpLxzlWm2NeWFiYcodash1dyzkkrimVJiFJkvAEY9iME6W8+vp6fFEoqchn50q73iTi8XRjMpkITKrtnmob43DPGJuXFeAKxHD7I7x3RwVviiupRRWV/3mpl6N9YwCsLrchIWE0SNjMBrrGVTZW2/jUjRv492c7ONI3TrHVwEevXM7lq2Zu7NhcU8jmmuQZZIPBMEXXrbm0tre30+X08oPDgqgK4UnjoPuePst168oozstOUmwhJEuckKM1H6UiyIkneiAQuOisqDVk5Yw+H2hE186+WvvpTBnMVEJ3IQTd3d0MDw+zZcsWzp8/n/J64okef67fuXPnNEOClDP0wVHG/BG2b1hJntWKw++nLN88rUkkFJpobT137hxPHhrDEZaRDUbMRgNVhRYsJsOUz/mZMy4O947qDjRnnQF2ryjmaO8YR3q8GCWV044QR/vG+OLb1qf8GaQDrbutrq6OrldOYTKMEFUvfCYGCXqcY2yuL8tKaJvJ3VRrPkqckKNZUcXPh48nujZm6mLEkotaNBgMBsLhMEeOHKGwsHDWsckwd7JME5MYjUZ27dqlz2xPFfFNMPF19pnsiuaSzLa1tVFtDLG8PJ9zrhDOgI/KApOu/oqH1WqltraW8qpleF87ipCi+MNRXONh+jwBrmsws7nSonfddY4EsMWRP98sE4oqSJLEuqp8DGoEFZnvvdzL+qoCfRBjtlBXZEJJct8Luvo5OHR+Xr3scyFbYfNMgpzh4WHOnj1LKBRiYGCAkpKSBZtOSJJUCvwCaAC6gPcIITwJj6kHHgSqARV4QAjxjbme+6I5UEQiEc6fP099fT1r166d864/244eCAQ4cOAAZWVlbNq0abKklZ4LjCzLhMNhDh48SGFhof48yTBb6B6NRjl69Cgmk4md27eyptSECqwst2ExyHz9d+f5+aF+zjun2yN7g1GWFVsYj6j4o4DBgCTLvNYX4ExbGwcPHuTs2bPYjQqBqKJnfQMRFZvZiNMXIX/yzG0ySMiSxPD49N70TMNulfn8dXVYjbLeZPOt925h9/Zmdu7cSWVlJWNjYxw9epSjR4/S3d2Nz+dbUMZ6sc7HmiBn/fr17Nq1S4/uXnjhBd75znfS3t7O/v37GR8fn8/T3ws8K4RYAzw7+e9ExIC/EUJsAC4HPi5J0sY51z2f1cyG+YRlfX19DA0NUVNTk3ISb6bXcblctLW1sWnTJr20AvOzcNZyBKnMaw9GJs7PeSYDeeYLZ7Zjx46xatUqqqsnElFdYwpFFgP2PBMv94/hCUR5pWOE804/tzdVsaW2mKiiMjqZWLMYZWxmA6X5ZqKKIBJTcAQlqhrWUVVoZnR0lC0xF0fO++gY8GM2mzCZzTzb5qJ/NMSgN8zKYgMWZFQhqJy0gG7p99LlnmiCqS624PZHWV5ipTR/4aYQQgiuWlXMTc3LcfkjVBZYdGvqxGOKNmFVOw/Pt8llKWr3Ws1cG8+dl5fH9773PV555RV6e3v5+MfT7nHZC1w9+f9/BDzPhVHJAEy2vg5O/v9xSZJOM6Fki5e1TsOShu6aNbSqqqxZs4ZgcHbTwtmgmTs4nc4Zz9GpEn1gYACXy8Xq1atTsp9y+KK82u2lZMSILMGeVaXYRDBp4k6WQFFVXONhQjEozDNTbDNTajPxYoebynwTDx7oxxOciFZWltloGRgnFFXwBGLkW2S63EF+9Fo/f3PdKj2J9OW1a+hyjHGy28EPDzkpNAkaik10jsbocCssL5G588rl1BRbefjIAA8e6J+opYeixBRBWb4ZSYJ/vGXttIks6UIrr1lNBurss5fV4iesqqqqn4d7enp05VpZWdmcDq2pdFVmG9FolLVr13L//ffP9ymqtB52IcSgJEmz7nqSJDUA24DX5nriJSN6MBjk+PHjLFu2jOXLl+NyufD75zfdI95McqbafSqRhjbPLRAIUF9fn9KOEompHO4PYDNJVBVZiMRUnjh8jo02P7sTGnKEEGyqLuCxky7CsgVfWMVuM1NXmodRkib82086GY+oVBeaJr3d/Lx1QzlPnXJSYDFgNshUF5np8wQ51udld4MdmKiJNy4rwREUFBYGKbUZiUairJMEQ74oH90I64uieMYDPHign3yzkZii0h+KgQCpABDwL0+fZd9HdiAvIGE234YZWZZ1a+ZVq1bpyjXNoXW27PdSNOkkHjVSUa5df/31DA0NTflZa2vrSeBz6by2JEkFwD7gHiGEd67HL0noniy8Tnf+mgatrq15yc8X0WiU48ePY7fb2bp1K93d3SlFAOGYigqYDRJCFQwP9OPzRdh0xbZpJI/FYuzespaaGi+/P9XPaLsbSySMwxlDMVh4W3Mt/3fSQUWBBVkCgwEMhih7Vtlpc/gJxxTsVhPlk0MT/JHpn5dJlhjxhwlHFcoLLMgWmQZzhDX11USjUc60nCIcCmGRTIyFJ6aeCmBgNESdPY9gVGU8FFtQGSxTpEtUrsXbUQFT7KiWeuYaTCjX5iqvPfPMM8l+vBlAkqRhzTlGkqRlgCPZgyVJMjFB8p8KIX6ZyloXdUfXWmPdbve08NpoNKY97ywWi3H06NGUZKqzQZukunr1aqqqqoDUS2ZWk4zFaMAfCk8MBLDYaFheT6H1wo6jKIpudSRJEssr7PzJW+zcvDPCyx0jOD1eygxBYoNnMIRk+gJm6soKQZKRJJll9gKuX1/B8+0j2PNNBMMxhBDUF5tRFEU/K/aNBvnPF3tQFOgaCdLrCbGhOp8/3VqM1WqloqKCuvrl/LzzBN0uP65ATHcvUISgZzTI2or8CfeZBSAbu2ti9lubt6a1tIbDYYaHh1P2Y88EEgUtGRjesB/4APDlyf/9VeIDJo0ivwecFkL8e6pPvGhEj0ajtLS0kJ+fz44dO6bdfdPpdBNC0NnZSTgc5qqrrlrQF6tp5JuamqaEXamKWkwGmQ3lRn7xmptCexkry0p4y9pyzEZZL8/FkzweZflm3ta0DFimv69ah4cHft/Jqa4hBPCWRjulpih3NC9DEXCga5Q8k8yH9yxnVUWB/pmNBcL89LU+ghGFtVUFRBUV53iYHcvt1BTG1bNliftuX8/f72/D2TOGxSihaP0CquDWuhjdXV2UlZXN6ugyGxYjjDaZTFRWVlJZWYkQgtdee02fgacoypRad7Z2+mTuMsuWLVvIU34Z+F9Jkj4M9ADvBpAkqYYJd9hbgDcBfwq0SJJ0bPLv/n5SATcjFiV093q9nDx5csqOmYhUe9e1PnOr1UpBQcG867DazWJkZCRpY85sRhXx6B9y8syJHsqK81lWVYqiqoRjik5yLUmUyoUvSRIrqkr5x3fY8fijGFGJBsbo7e1lfHyc5qIirruqgrKyMv19G41Gfnqgj8dbhukfCyGEoNhqxGiQJtxaowqJVdTKQgufv6mRjz10EptJBkkiHFVQgb1XNhH0jemWxoWFhbr4I9Us+GKflzWX3xUrVug6dY/Ho9/E8/Ly9KTeQgQsiUjmLrOQHV1MzDy/LsnPB5jQoyOEeJHk1lKzIus7en9/Pz09PTQ3N8/aNZQK0TXHWK3P/ODBg9M+7FSgKAotLS1YLJak0QWkFrr39PRwsK2PgpJKCg1RauxWfOEYR3vHqC406yWfdC96s0GmarLL7bWREP/6SojxEKytiPChpjG6u7v1FtSekJn/axme9HyDdoefzpEAtXYrwajC7hVFxGKj+vFBe68NZTbesbWaXx4bQpJACPjkNQ0U5Vspyrfq4g/tXNzX14ckSSllwZciMRaPRPNJrT33zJkzRKPRKQKWhez2yXb0S6ozTpIkvXQWjUZT8mqfi+ja3XnLli36GOZ0a+NAyh5zs4XummVULBZjw6aNDJ8aRKgTjSiyBNHJHX2hIWOnK8BnHjuFEBPWyod6fcSEzHfev5tQKITL5eLQmR58viA2yUyhyUyt3UKPO8RYSKG8wMz4+DhWZZS6ujoURdE/Y1mW+fAVdbxpVQlOX4QVpRNGGImfQfy5ODELrtW8S0tLp3y/S030eGi2zPn5+VO88uPHRGslynStprNwRs8askJ0rXQ202STZJiJ6PEJvMQQO12pqqqqHDlyhE2bNs3pWTfTTSQajXLs2DHKyspYuXIl46EYRoPMWEDB5g/T0u+lstDMc+0jXLayZIoaLF282ukmpqiU2CbesynPxIn+caKKgtVqpa6ujp2hPF5xnMdslohEojhGQ5hlaCwzEY4qfOelAf7t3c3Y8vNhsnNO290BGsssrKucbrsUiCg8cnSQYW+YXSvsXL22bFoW3Ov1Tql5a4RZbI/1dJAoYIkX44TD4bTkqjM5wF6MyDjRhRCcPn2atWvXpmUAmezCiNd9z5TAS3VH7+3tJRQKcdlll6Xk6ZXsuZNl54vyTNywrpTnT3rpGglgkCWKJ00bh7wh3r29Vu8KSxWhqIIvrGAyyAgmJqnKkkRUFRgNEsa4z2HPqlIO94zxWqcHSTKhSFFWl1uJhkNEowpDPvizB4+RbzHwqWtXs3drzRRZpUZ67f8DRBTBB3/SQq8nREwVPHZimI/sqeeDV1xQ/kmSNKXmrSm+Ojs78Xg8nD9/nsrKyoz2s8+EhbTOxotxtDl4IyMjnD9/HpPJpEcsyTzoFuoAu5jISjJu+/btC3ba0Ei1cuXKGTOZqezoWpitnc1S9fNK7F/Xav/xRweYuMiq7Pk0WEOc7Q2zorIYq0Eiv9DC4FgIlz9CTYKIRFEFr5x30+bwU5Zv4pq15Xrd+njfGD98pZeoomKQwWKQGPKGMBoMGCX44BVTdfkGWeLua1bS3VxNJKbyL0+1Mzruo8Bioj8gEVZjGBBE/DH+3+NthD2DvHl9DWVlEzu0dvPUyK6qKn9odzIwFkZCYDZIKELlv17q4c8mhzAmQ7zi69ixY1RUVDA2NkZXV5fu7aaFx5ne7TN1VIj3kIcLKsLz588TDAaniXFyZ/QUhw7OBIfDwblz5+actT7Xjq653VRUVLBhwwaOHTuWcqifzHoqsfYvhGAsECYUFWzfsZPDgU6i0TC9fX0gBH7JSjBQhCiyTLkQn2od5oWzIxRbjXQ4/Zx1+Lnr6pWEogrfe7mHQqsRo2zk5Q43EVVQWWghHBO8e/syPnJlw7S1StLEfPJIJMLNNREeOmskhJGxYAhZQh+jHFEEh0ZM7JocUgFQVlZGeXk5hYWF+s6riInHS7I00TUnJurs4UgUi8mYUu7BbrfruoV42W0oFJq3m8tMyFazjKYi1DzotMmq2mAJg8Ggz9GTJGlBoXsqyrW4xxqAQ0C/EOK2VJ7/opGpwgRxzp07x+joKDt37pxz951tR/d6vbS0tEyZwZZqbRwu1PW1umyiRFUIwaFONwe6PUhAgdXE1uVlHO8fI7+siEA4ykqLwrijj1e72rHb7ZSXl1NsL+GlDg+1xdbJMH/C373HHUSezH7nmQwMjE2EzRaDPCF0ial0jcysBdDceG7Y3sjVlxXQ4fRzz8Mnp2jCEQKD0cjKlSv15Jo2EUVLrlVUVLC9vgijPDGgQZ6s/+9ZacdkkKcl9JKZISbusImEiQ+PzWbzvJNhGhajKy6ZGKetrQ23243D4eCXv5xoUAsEAvMt4WnKtS9LknTv5L8/M8Nj7wZOA0Uz/H4asrajp4toNEowGERRlFltoeMxk8uMNtNt69atU0KpdFxpFEXB5XLR0NBAQ0PDlPUoisLQWJDXujxUTxLW7Y8wGohw+5ZqhsbD2POMrKkswGSQL8xAdzo52XYWj1vFSgFF+TaiqkT/aIg/nHWxq6EEIQSRmDo5+FBgMskYZQlhkIkoydc+NjbGqVOn2LRpk36sWFZs5famah45OoiiTiThrGYDb9964RhkNpt1QYkQgrGxMVwuFyMjnfz1djM/b4/hjcAVq0r5zI1rsJgNepQTf6aP787TypIzfX+J4XGyMdHplr6WQrlmsVjIz8/HbrdTWlpKMBjkmWee4W1vexulpaX83//9X7pPOadyDUCSpDrgVuA+4FOpPvlFsaNr53GLxcLq1atTvlEkdtNpEYE2KCKxwSPV5J3P56O1tRWbzcbKlSunPL92jvVHFGRZ0v3N7TYTzvEwqyryWVUx9ZwmyzKuqIn/7YBwtASzLUzfWBhcXto9CiajkcPdcHLQx5sby/hDhxtVCIQkUV1kIRhRGA1GuaN5uueaw+Ggs7OTrVu3TtsR771pDQZZ4ndtLiwmmb96SwO7G5InSCVJ0l1TGxsbaQ6FuGytC5fLRSg0Sm/nOcrLyykpKcFgMGAwGDCZTDrhtWx+LBabkuCbi4B5eXm6zDOx9GW1WvXdfrZdcqmUa9oZXZIk3vKWt2Cz2XjxxRdnHTA5C1JVrn0d+DSQVtZvyYk+PDxMR0cHW7Zsoa2tbdqIm9kQv0PHYjFOnDhBQUGBPhM9EakQXfOqW79+PX19ffrPE9tZi/JMqEIQU1SMBhm3P0pVUfKL0ROI8JMD/RRYjJTazBhkKMizYJTBi4/VJSai4RAjnnFO4ecTl9XhVizsb3HQOjCOIgTv3VHDrZunEr2npwen08n27duTfmZmg8znbl7L525eO+dnmQitfKdloz0eD06nk7Nnz2K1WnW/OKvVqpNMURS6u7v1I5cW5sfv9rMhWelL8+mLRqP6bp/Y1roUOzpMz7rDhbp9MiRTrgG0trbuTeX1JEm6DXAIIQ5LknR1OmtdstA92e47Hwvn+EGLDQ0Ns/Yaz0Z0zV/O4XCwa9cundTa77RdS+tZryiw8ObGMl7umMiXFNuMXL02uXbdOR5BnfRwB6gstDIwFqK5rhhvSKGowAIF+ZjyY1iNgnDQz7dfOEdYkajItxBSBd3uoB49CCE4e/YskUiE9Zub+Pfnunixw02e0cBHrlzBDRsqkq5jvoivkcNEdtnlctHa2kosFtN/53A4iMVibN26Vf+std09lbN9IuKnrGqus/FtrUtdt48neiodmjMo1wB+laJy7U3A7ZIk3QJYgSJJkn4ihPiTuda6JDt6NBrlxIkTFBUVTdl90yW6wWBgdHSUvr6+lActJiO65gsnhND17JFIRLdmSiS5hs01RTRW5BNRVPLNxhnHFOVbjJO+7AKDLOEPT4w62l5fzO/PuRkNRDHIEmPBGLdfVocwyZhsfqpsRsKhEFIoyO9aerimKkp1RRl9fX28NixxwCHo/d0hIopKrd1KTBH8x3PnWVZsYXNNynmatKF1mml95YmkHx4eTlq+S2zWidcBpLLba1GE1tY6MjLCqVOnCIfD+rVQVFS0aLt7PLkzUFqbU7kmhPgs8FmAyR39b1MhOSwB0cfHx2lpaUkqcEmH6EIIXC4Xbrebyy+/PCUFWzKix5fg4pNuWoY+FovNeiFaTQasptnv5DXFFq5ZW87zZ13IkowswZ9eVsfK8nw+flUDT59yEFVUbttSxcbqAl4+7yEUmzjf2vLzMVnziJki2IsKaW1t5bBD8Os+maI8E25/BEUI7HkmCq1GxkMxWvq9WSV6PCRJYmhoiLq6OlasWMH4+Dgul0sv32nkLCgo0EtSMHOzTvyQy9leU7vZaKYl/f39DA4O0tbWRn5+vr7bpzsHLR1k2AE2FeXavLGoRNey4U1NTUnrjakSXVEUWltbiUQiVFVVpSxTTSS6lgRcs2aNXoKDC51W4XCYU6dOUVExVTGWLiRJ4oYNFWyuLcIfVqgoMGOfHEO8tqqAtZPz0NuGfXz60VOEYypDYyHGghOz1xRFsHdLOX29PWzcuJGn3E4KbeMYJRUZlagKbl+IPKMVSQK7LXsXdzw0s45ly5bpph9ab7zmEKN1y/n9foqLiykvL9d745M168Rn8lPd7bWBDKtXr9ZHK8fbM5eWluq9ApkM8RM93bOtXEv4+fNMZOZTwqKc0TWLJr/fnzQbriEVoocmmz2WLVtGQUEBw8PDKa8rnuha0i1Rh64l3QAuv/xyvF4vLpeLrq4uTCaTropKt1YqSdK0Drl4qELwzec6McgSlZOz0DpHAlzeUMLGChNGTzcbN2+mqKiIQqsHBZmiPAsrK0y0DfuIqeDyBqnKgxoxwsiIgZKSkqyFseFwWM+LzGToGV++0xpOXC4XnZ2dmEwmfbe32WzTQvzZynfTPru47L4kXRit3NDQoM9ci5fdagq8TExY1a71i9nTHRZhR9fGHNvtdrZt2zbrHXUuoo+OjtLa2sqGDRsoLS1lbGws7TO9oih0dXXpSbf40C6ZUUR8ySkYDOJ0OvXzqHahZmI6ZzCq4IvEqJock2wxGSgrsLC+RMLi7aNp2za9fPa+nbWc6PfiHJ8Yk7y2soD37KihusjCjuXFBMYnCNXe3o7NZtPXmSnnFU20tHbtWr0ePhcSG060+nlbW5teP5+tfDdbQm+2Ml7izDVNdnvixAkAPcSfy3xyLlzSRNfO442NjSnZOM9GdE3Xrk1ThfnJVAcGBvQBEYklmpmSbhry8vJYvnw5y5cvJxqNMjIyoptCFBcXU1FRQWlp6bzaOm0mA+X5ZkYDUew2E+GYSigUIup18Kbd2zGZTPS4Azz4Wh+He0YxyhLb6ovZXl/EmxrLqCi4QGJTSQm9AQO/PivoavNTahng5vp+is0XzszzDWPHx8c5efLklOac+SCxfq6V77Sbk9aaG1++mymhF41GUzb2mI/sNhVczMo1yGLoPjg4SGdn54zn8WRIRnRVVWlvbycUCk3TtaeTvItEInR1dWG1Wtm0adOUC0MzboTZk0DxMJlMumRTC0udTicdHR26P1s6u6gkSdx97Sr+/dkOHONhwqEgt622cN0V25BlmWfbnNz3VDtuf3RCbGI00DUSxBeOcfW6C/mFYFThk/97ksM9o4RjKrIEhRYTHaNmfvinWwiNj+otr+nenEZHRzlz5gxNTU0Z3b2SZdS1yElRFP2MrdXP4xN6kUgEh8NBXV0d0WgUIYTexDLXd5mq7HauQYuw8DN6tpEVoodCIRwOB7t3707rzmgwGKbYN2nJnpKSEtatWzftw051Rx8fH+fEiRN6ll97nrk83VJFYljq9/txOp20tLSgqirl5eVUVFTMGR7Wl+TxlTs28OqRFkoLy9i0fmJiTTCq8J0XughHVQwSRFXwhRWMBnjpvIdP//IU33rvFsxGmZ8f7OPM4DiRmIrERO98VFHxhqK0DAa4as30M3NHRwcWi0UnW7Kec6fTqbcVZ9KOKRHxGfWGhgZisRgjIyP09/frgzI1JZwkSZw8eZK6ujo9NI/f7WOxmH6uTyWhlyi7jR8sUVxcrA+WMBqN00RbF7NyDbJEdKvVSnNzc9p/ZzAY9J01mfY72ePn2tE1JVxzc7OuooLMkTwR4ZjCc+fH6XAqVBVVc926EmIBr555LikpoaKiImmiLBqNcuL4cVYuq5oy9dUbjKEKgdkoE4gqXGh5n/CFGxgLcc7pZ+OywgnhS9xbkYDYpLAlvswff3Nas2YNgUAAl8uluwJpoXNxcTFDQ0P09fWxffv2jCSw0oHRaJx2xnY6nXR3d+P3+6fcQGcq382nWSdxsIS222uyW+2mrh31fD5fWv4L8UhVuSZJkh34HybsoQXwISHEK6m8xkUjaoELLa2ZkKlqk1tcLpeuhItEIlOyupkmuRCChw4NcKLfiz3PyKA3TLc7xD3XrtQvmPizaH5+vr6LKorC8ePHWb169ZRSH0BZgQl7nolYbMJzXUyaNJtkmRKbkXBMoL2FTTWFvHB2hHyzAX9EQRUgSVBRaGHHCvuMa7fZbHr+IRaL4Xa76e/v5/jx40iSxJo1a5bcNUY7Y1utVkZGRli/fmIybHz5Lv4okqlmHVmW9aTs6tWrCYVCDA8P67P5+vr6aG9v58orr5zvW0tVufYN4GkhxLskSTIDKc9oXvJe93jIsozb7WZ8fDwlmepsnW6tra3IsjzFmSa+LXO2pFsyqEJwsGuU4/1erEaZq9aUTfNYC0QVTg54qS2e0J8XWCbIPjgWpqHMNuXcp9V7XS4Xhw8fJhAIUFtbm3QAgFGW+Ydb1vKJX7QQUwUGCcxGmYpCM/6wyvrqAhonhTTv2lbD6UEfv2tzIoB8s5FbNlfykStXkDdHY4/+epPmil6vF7vdzvLly/Wzq2YiUVFRsSSzwMPhMMeOHaOxsVFvya2pqZl2FDGbzVPKdzBVGzFTs04qORotBzM+Ps7GjRuJxWKcP3+eF154gf/93//lG9/4BmvWrEnnbc2pXJMkqQi4CvgggBAiAqQ8MTNrRE/XfCIWi3Hu3DlisRiXXXZZSh94MpJqF0J1dTXLly+f8hhZlnXzgNLS0rR2qIPdozxzxklFgZnxUJRfHOrng1cs191aAYyyhASoYmIeuNZCm8yVRav3hkIhJEli586d+Hw+fRSvloDS5JpHesdQ1IlZbALBiD9KY0U+uxvsvGt7DaZJcwmDLPGF29bxyWtWoghBeb457Z1YswOTZZmmpiYkSaKkpITGxkbdlFIriyWuM5sIhUIcO3YsaVkv8SgSDAanrFM7MmnrTGzW0cL7VEN8rVlGlmX27NnD+vXr+fznP5/yvL4EpKJcWwU4gR9IktQMHAbuFkKkNMfsotjRg8Egx44do6qqCq/XO+8LRku6rVu3jvLy8im/UyYNFVetWsXw8DDt7e0UFhZSWVlJWVnZnFnnk/1eygvM5JkN5GHAF1HocvunEN1iNHD12nKeOePEYpSJKIINVQXU2pMnr7Qpstu3b8dsNlNUVIS9ogqjBN5RD0NDQ7S1tVFQUMDTJ0JYjJLebltoEayusPGnl9Unfe75TkVVVZWTJ0+Sn5/PqlWrpt0k4lVtiqLgdrsZHh7WW0+1LsJMt55qtfv169dPmZI7E/Ly8qivr9cFMZpBRFtb27TeAlmW9UlBqTbrzGQMuWLFiqTrmUm5dt9996X6ERiB7cAnhBCvSZL0DSZC/H9I9Y+XFG63m9OnT7Np0yasViseT1L3nDkRn3SLL3PEn8dlWZ7i962VxM6fP4/FYtF/l6wkZjUZcAci2JhUK6lCt2iKx82bKqm1W+n1BCnLN7NjhX2a2EVT7gWDQbZt24bBYGAsGOX/++05Tg/5kCWJP7u8Dm+oiEdP+lGVAKoSYzwYRURljCYjMZUFOcwmgyb1raiomJIMnAkGg2HK56kdReL73CsqKlIqT80Gzc9/48aN8xq9lbhOTX2nVUVKS0upqKjQBTEzae21/68ljdNxgJ1FuQaQinKtD+gTQmiTUx8h+fz0pFjS0L2np4fBwUF2TE4d1UwL0oFmBz0yMjLtXD9b0i2+623NmjV6SUzrmEq8SN+ypoyfH+ynPxxCFVBRYGFd1fREoSRJNNcV01yX/ILU8gcWi4UtW7boa/rP33dxeshHWf7EFNVv/O48IFFeYALZwEhYAaOZIKCGFGwGleXKIGfPRqioqKC4uHhBZIpEIhw/fpy6urp5jRWKbz3VmlG083IgEJjW+ZYqfD4fLS0tbN68OSMOq1pffEFBwZQWWa3xKb58ZzKZZkzoBQIBJEnSS3gLbJhJRbk2JElSryRJ64QQbUz0xc86Ez0eS7Kjq6rK6dOnURSFnTt3TlEspevTHgqFCIVC0+ygU+l0i0d87Va7SDUzQ+2O/4Er6uh1hzAaJNZWFaSc3NKgyXMrKipYvnz5lN+1Do5jzzMiSRImg4Q/rGAzy/rZO99iZHWFjctXlmKSJa5aU0aRRdaz46dPn9Y931I5isRDO/s2NjZOO/LMF2azWXeF1aoN8c4xqTQUaV14W7ZsyVozSmKLrKZtiG+a0W742m4/MjKCw+HQb9SRSITW1taF3GhTVa59AvjpZMb9PPDnqb6ANMeuO28r12g0mjQjrokhKisrkw53ePnll9mzZ8+cz68l3YLBIFddddU0kqfb6TYT4s93Xq933mQKBoO6fXWyduC/eaSV/rEgxXkmhBCcGvRhMcrUTJ7vPf4oN2ys4O5rViV9/vijiNvt1rPOcwlwtLB4w4YNKZ19F4r4zjeXy4WqqjqZ4ttyvV4vp06dYsuWLUvWiKJ51TudTgKBAHa7HYvFgsPh0PMqiqJw1113kZeXx7e//e35utpmvW6ZNaInC8M1Z9ZkyTINqRBde57169dz7tw5duzYccGqOGFEcSYRT6aRkREsFguVlZVz7kyHO4b41YGz1FRXcdvWeupKpneenXf5+cfH2ybmrauCDdUFnHUG8IUnblhFViNfe9fmKcm/2aA1wDidThRFSUomzVQymzvmXNA0Ay6XS9cM5OXlMTQ0lNQHb6mgqiq9vb10dnbq3/Xzzz9PZ2cny5Yt4ytf+cpCNpU3DtG13ve5hi3ORXTNY057nkOHDrFlyxbMZnNWmmBmg3audzqdwMS5vrKycsr7e+FkF//8605CwghILCuy8LV3b05K9tFAlA6XnzyTgfXVBYwGohzsHkWSYNcKuz6aKV1oZHI6nfh8Pn1nGh4evqjIJITQyWQ2m/UE6UxtuYsJrc9/27Zt+q7+yU9+ktbWVux2O3fddRd//ucpR9KJeP0TXfM38/l8NDU1zdn7PhPRtaSbx+OhublZb8U8evQo69atw2KxpDWiONOIRCI66bVzvSRJfPHZAc56JfJMRkDgjyi8c+syPvPWtBoqMgZVVens7KSvrw+z2UxeXl7aApxsQRvysHXrViwWi14LdzqdRKNRPVey0MRjutBIrvX5q6rK5z//eUKhEN/5znf03oLEvEsayPqbyWrWPRaLcfz4cYqKiubUoscj0RdcURROnjyJyWRi+/btU0IkWZ6YY65lSJeqTdNsNutDCmKxGK2trXi9XpxBFaGCxKS4QoLzI/OyA84IBgYGGB0d5U1vehMGg0E/L89UbVgsOJ1OOjs72bZtm145ia+Fx7flJopbstl/PzY2xpkzZ2hubsZqtSKE4Itf/CJer5f//u//nrD7mmwfvpiRNaL7fD6OHDnCqlWrqK6e7kc+E7Q2VS2poSXdli1bNu3DFEJQWFjIyZMn9bA503ZB6UKb9Wa1WmlqamKH5zS/PeUkElVQ1CgxFWptgkgkklU/s0Rovf9er5etW7fqn2+yakN8SWwmAU4mMTw8rHsNzERao9FIZWUllZWV07Lj8TLXTCbutISgdrwRQnD//fczODjID3/4w4yMk1osZC10d7lcCCHSNic4ePAgzc3NmM3mKUm3xLbC+KSbNlVFO4OWlJRQWVm5KG2Z8UhWPusfDfK3+1oZ8oYn7KSKzNxzuR3hn2gM0ho5splZ1qy8YrEYGzZsSOkziRfgeDweveutvLw8ozvo4OAg/f39bN26dd6efFroPDFsIjSt3XU+0Ep7zc3N2Gw2hBD8+7//O62trfzkJz/J9ITY1+8ZXVXVKdryVHHkyBE2bNjA2NgY58+fn5a8m0t5pqoqbrcbp9Op2//OpxyWLjQvu4aGhmmyWud4mCO9Y0jAjhV2yibbUxPP9VpmPJNnUM3K2mKx0NjYOK/n1bretJKYLMtTQvz5or+/n6GhIZqbmzNGHM2txuVy6TcobbdPNYLSmnQ0gw0hBN/61rc4cOAADz30UDaOCpce0Y8dO4bZbCYQCExJukH6GvLEcpiWeKqoqMjol6Xd/ZPVoj2BCPuODuIYD9NcW8xNmyqT+r8riqJnxhdSr098zhMnTlBSUkJDQ8O8niMZwuGwTvr4hqLECSqzobe3F6fTSXNzc9ZuwFq7q7ZWmGo/nez6SUbyBx54gOeee45HHnkkW8etS4voiqLw4osvYrfb2bJly4I63ZJB25WcTueU/ueFlG5GRkY4e/Zs0sYOfyTGZx49jcsXxmKUCUZVbtlUyQevmD1xo92gHA4Hbrdb7ySrqKhI+ULT3Hm07rRsQWsocjqdjI2NUVhYOKc9dnd3Nx6Ph6ampkU9Wmk5CJfLhd/vx2636zkIg8GgNw9pfQVCCH7wgx/wxBNP8Oijj2bTWefSIbrWhinLMo2NjVNkiJkgebLXczqdOBwOFEWZUgNP9fn7+/sZGBjQcwqJONQ9yr8900F5weQsMlXgDkT56Z9vn3GqSzL4/X4cDoe+K811rtcSmDN14WULWpJMi6A0S+f4m2lnZyfj4+Ns3rx5SealadAm3Go5CJPJhN/vZ9OmTXo+6MEHH2Tfvn3s378/23X81y/RhZjILKeCsbExPfR1uVx6MgUuJN1g4e2sMyEajeJyuXA4HASDQUpLS6msrNTPyqOBKANjIWxmAytKJ77w8+fP4/P52Lx584yh56HuUf71mQ4q4ojuCUT5SZpEj0c4HNbXGg6Hp53rtTnp6VgxZwuJdXCtVzyb4fp8EAwGOXLkCOXl5fh8Pn7605/idDrp6uri+eefz4iYZg688YkeP8vcZrPR0dFBfn4+VVVVi97pBtN7231yPk90KshGE0LArhXFbLGNYTIakxpWxsMfifH3j51h2BvGbJQIxlRu31I1o4Z8PmuNP9fbbDa8Xi9btmxZlL71VKFl/X0+HxaLhfHx8UVLks4FTee+YcMGXQL7k5/8hB/84AesXLmSkydP8uyzz06z98ow3rhEF0LQ0dHB2NjYlKyrNhFFs1FeTJInW+M//uokYz4/BiWCwWhkeDzKB3dVcc322UmuYTQQ5bHjgzh9EbbUFHHjxoqkjjMLhdvt5tSpU5SUlDA+Po7VatX78BezXp8IIQRtbW0A+o0xmWZAK91l02E2EdpxMZ7k//d//8d//Md/8MQTT2C321OakpoBvH6JDhNhZjIoikJLSwtWq3XartjT04OqqtTW1i4pyWHiIv3bX56iqtCMqig4HA7GYgauqZXYWHkhQbaYF2cyaOYZ8d1b8dlmSZIyUg5LF5olldFonNVcMl7NNpMAJ9PQSB7vWPP000/z1a9+lSeffHKxjz2vb6Jro4fjoX3Amh3RlBebvNOfOnUKk8lEZWXljI4vi4X/frGblj4PhtAY+cWlBFWZv71+NXaz0JN5QoikgpZEqELw49f6ePTYIAB3NC/jzy6vW9AOPzAwoDeczFQy1MphTqcz6bk+G9Dq91arldWrV6f8Olq+xOVy6QIczdk1UzmacDisayQ0i+Znn32Wf/7nf+bJJ5/MiCb/6aef5u6770ZRFO68807uvXe6Gczzzz/PPffcw/Hjx08BLiHEWxb8wjNgUYken3RLvGMmasiDwSAOh0NXhlVUVFBZWbnoKqauAQf/9bs2/MYi8q0m3rerlubaqe4xWtnG4XDojS+VlZXTZrI93jLEt1/ootAyEQqOhxU+dlUDtzel3iIcj+7ubtxuN01NTSmHl9q53uFwZGSUVDJovnMFBQWsWpVcP5/q82iZcbfbjc1m00P8+R5HIpEIR48eZc2aNfo1+Pvf/57Pf/7zPPHEEzPOEEgHiqKwdu1afvvb31JXV8euXbv4+c9/zsaNG/XHjI6OsmfPHp5++mmWL18uSZJUKYRIZiGVESwa0QcHB+nq6tJbCvUXSKEJRtuRHA6HPtywsrIy6xpqbbdsampCMpowytKcu28ikex2O5WVlZSUlPCPj7dzvH9M93rzhWNsriniS3s3pLUuzXMuFAqxadOmee908aOk3G73FCXbfImkqqrepDOTUeJ8MFPzSzoCHI3k8VbRL730Ep/5zGd4/PHHM9Zv8Morr/CFL3yBX//61wDcf//9AHz2s5/VH/Od73yHgYEB/uVf/gVez+o1DdpFOT4+Pm12WqqdbhaLRQ/1tdCuo6ODYDA44+650DV3dnbi9XrZvn17WjudwWDQxRfajuRwOGhvb0cJSITCCvnmidlgMUXo7bDprE2zYt68efOC3nO8RXI8kbShDVoOIlX/dq0Tr7y8PCVzyXQQ7/WWzJNO686bqb89Go1y7NixKXbMBw4c4NOf/jT79+/PaFNRf3//lPdfV1fHa6+9NuUx7e3tRKNRrr76al544YXDwDeEEA9mbBEJyCrRtekjNpttmkx1vtNSTCaTPipH2z01Yz+t/m232+dNAE19Jssyzc3NCyZSaWkppaWlCCGoXDHC6cfaGPb4QJKw28y8Z1vqDS2aXFczYMzk+TqRSFoUpfmiz3VDVRRF99Ovra3N2LpmQqInXTLbaU2AE41GOXr0KCtXrtTP30eOHOHuu+/mV7/6VcZvSsmi5MTPLBaLcfjwYZ599lkKCgreCrwiSdKrQoj2jC5mElklemtrK5WVldO++Ex1uiXunm63m8HBQc6cOUNxcTGVlZVpJXE0u+PS0tKkfnYLgSRJrK4p5wcfLOZQzyjBUIgV1ghD588wdB498TjT7qlp+ysrKzN+YSZDfBSlDTqcaUR0LBbj2LFj1NbWzstBdqHQRDbaNFat1fno0aNIkkQoFKKhoUGvhZ84cYKPf/zj7Nu3L6MaAA11dXX09vbq/+7r65sWMdTV1emyWiGES5Kk3wPNQFaIvujltUwaN84EIYQeMrvdbgoKCvSa8kxheCgU4sSJEyxfvjwt/XwmEJ+DiEaj+tlTKy9FIhGOHTu2JGtLhHauj+/DDwQCNDQ0LMpOng60XbOwsJBwOMzzzz9PS0sLhw8f5rHHHmPTpk1Ze921a9fy7LPPUltby65du/jZz3425fVOnz7NXXfdxa9//WtMJlM+cAB4nxDiZDbWlNUdPX7aabYGGyaDNkJIO3uOj4/jcDjo7OzUG0niFWw+n4+TJ09OKbcsJhJ3T5fLpY/rLSoqwuPxsH79+oxZMS8E8ef6cDjMkSNHKC4upr+/n8HBwbTP9dmCdpRYsWKFfnMUQrB//36am5t5//vfz9e//nWuvfbajL+20WjkW9/6Fm9961tRFIUPfehDbNq0ie9+97sA/OVf/iUbNmzgpptuoqmpCSZI/j/ZIjlkeUeP941binbWZNAEIpqCraCggJGREZqami66QfZer5fjx49TWFhIMBi8aNpG4YJwZvXq1foNKLFer0UmmUyUpgKN5DU1NfpR4ty5c/zJn/wJP/7xj2lubkZVVWKx2JJ2Dcbh9d0wE4vFiMViFw3JE9Hd3U1PTw8Wi0XPMldWVi75bgTTrZgXS1ufCmYbdqhBO9c7nU79XJ9uzmQ+0BLAVVVV+lGiq6uL97///Xz/+99nx44dWXvtBeD1TfRoNKrX0i8mkmv+aaOjo2zZsgWj0UgkEsHhcOjnZI30i22SCBc07s3NzUkbhOJLYZnU1qeCdIcdwsyNL5m+SamqyvHjx6moqNC7Lnt7e3nve9/Lf/3Xf3HZZZct+DVS6XiDCUu0yy+/nF/84he8613vmutpX99Ef//7308kEuHtb387N95440URGmvlM4D169fPWHONl61mo1Y/E4aGhujp6WHr1q0ph5WZ0NanAk0CGy8CSRfaTUrT12uDLxfa9aiRPL6GPzg4yLve9S6++c1vcuWVV877uTWk0vGmPe6GG27AarXyoQ996I1PdFVVOXr0KI888ojW6sfevXu5+eab532hLASxWIyWlhbsdjsNDQ0pkSCx0y2bxpO9vb04HI4FeajF36QCgYB+k1poX7vmvpKpYYcaNGNHLZLS+vDTualq3XilpaW6KefQ0BDvfve7+dd//VeuueaajKw1lY43gK9//euYTCYOHjzIbbfddlEQPatZd1mW2bFjBzt27OBLX/oSJ0+e5OGHH+a2226jqqqKvXv3cuutty6KUkib+VZfX59WrTexVu/xePTGjKKiIn2++kJIrw2n8Pl8bNu2bUHPldhQFO+FrtW/011vNocdxs9bT6zXpyJoUVWVlpYWSkpKdJI7nU7e8573cP/992eM5JBax1t/fz+PPvoov/vd7zh48GDGXnuhWLRpqpIksWXLFrZs2cI//dM/cebMGR555BHe+c53UlxczN69e7ntttsoLy/PeHislc8W6rqiTdcsKyub4ut27tw53SxjNq+0ZND02qqqTvTUZ/C9J84F13oLtPWmYt/s9XppbW3VzRKzCaPRqE82jT/Xnz17Nul6NfFMUVGR3lc/MjLCu9/9bv7pn/6JG2+8MaPrS6Xj7Z577uErX/nKkldFEpHV0D0VaAYUjzzyCPv378dqtfK2t72NvXv3UlVVteAL3+Px0NbWxubNm7OWI9C6sYaHh3G5XCmbPmiz0vPy8tKScmZqvdo52WQyJdXWa6OIZkoKLhYS7aa1gQ0ej4eioiJdITc6Oso73/lOPvOZz3DHHXdkfB2phO4rV67UbwgulwubzcYDDzww13pe32f0dCGEoLu7m3379vHYY48hSRK33XYbd9xxh25EkQ60xFZTU9OimkMk1uq1Bp34NWgCEK3ddikRLwnWtPVWq5Xu7m593tjFhGAwSEtLC5FIBJPJhNvtRpZl/vVf/5V77rmHd7/73Vl53VQ63uLxwQ9+8KI5o19URJ/ywkIwMDDAvn37ePTRRwmHw9x2223s3bt3zkSadsPweDx6+WypEAqF9LKdEEI/c7a1tVFbW5tVK+b5IBKJ0NXVRX9/P1arVc/gL3bTy0zQ1Hsmk4nGxkYUReHJJ5/kS1/6EqOjo9x22238zd/8DatXr87K6z/55JPcc889esfb5z73uSkdb/HIET1NCCFwOBw8+uij7Nu3j7GxMW699Vb27t07zaJIVVXa2toQQsxYPlsqRCIRBgYG9LHA1dXVuq7+YiARXBh2qM1n01xcE7X1S/G5CiE4c+YMBoNB/94DgQDvec97+MAHPsAf/dEf8eKLL7JmzZpp7kUXOXJETwaXy8WvfvUr9u3bh8Ph4Oabb2bv3r3U1tby9NNPs2vXrozLODMBv99PS0sL69ato7CwcFoZbClGAsfD4XDQ1dWVdNhhvLbe4/HoQqF0k4/zhZa0lCSJtWvXIkkSwWCQ97///bz73e/mIx/5SNbXkEXkiD4XRkdH2b9/Pz/96U85duwY1113HZ/4xCemTXpZamjZ62R16ETb5qUYEjk0NERvb++s3nMa4oVCLpcLi8Wi5yGy0Tuu2UULIXQz0XA4zB//8R9z66238ld/9VcZuTnO1fX205/+lK985SsAFBQU8J//+Z80Nzcv+HXJET01BAIB3vzmN/OFL3wBn8/Hvn37OHv2LNdddx133HHHtJnqiw232017eztNTU1z9tFrtXqHw6EPidR6xLNVshkYGGBwcHDejTrx7bjzcaaZDZpDUTQaZcOGDbps9wMf+ABXX30199xzT0ZInkrX28svv8yGDRsoKSnhqaee4gtf+MK0Ovo8kSN6qnC73VNq5IFAgCeffJJf/vKXtLS0cPXVV7N3714uu+yyRa1xauFwc3Nz2m62iTPYbDabXrbLVLjc19end+Nl4nOZS1ufLs6dO0c4HGbjxo1IkkQ0GuVDH/oQu3fv5tOf/nTGjjmpdr1p8Hg8bN68mf7+/ky8/Ou7M24xkdgIY7PZeNe73sW73vUuQqEQv/3tb3nwwQe55557uPLKK7njjjvYs2dPVs+XmkY72Zk3FUiShN1ux263T6l9d3d3YzabFxwu9/T04Ha7MzoiaTZt/Vy+bono6OjQDTAlSSIWi/GXf/mXbN26NaMkh9S63uLxve99j5tvvjljr59tvGGIPhu0Jpy3ve1tRCIRfve73/HII4/wt3/7t1x++eXs3buXq666KqNKqq6uLjweD9u2bcsIiSRJorCwkMLCQlavXj3FyDFeGJJqzVszv8zmRFOj0Uh1dbU+dcftdjM0NKS3D8+mre/s7CQQCOgGmIqicNddd7F69Wo+//nPZzxhmUrXm4bnnnuO733ve7z44osZXUM2cUkQPR5ms5mbbrqJm266iWg0yu9//3sefvhhPvvZz7Jjxw727t3LNddcM++hEUIIzp49SyQSobm5OWskys/PJz8/n4aGBl291traiqqqs05b1frqA4HAoiYsE33dNG39+fPnp2nru7q69ImrkiShqip//dd/TVVVFV/84hezUpVIxecNJvzm7rzzTp566indTfb1gDfMGX2h0GazP/LIIzz//PNs3ryZO+64g+uvvz7l9k9VVfURRFoJaLERiUT0M3IkEpnmgX/u3DkikYh+5l1qJGrrtamrmv+/qqr83d/9HWazma997WtZuzGl0vXW09PDtddey4MPPsiePXsy+fK5ZNxSQFVVXn31VR555BGeeeYZ1q5dy9vf/nZuuOGGGfvltXlyxcXFKUtgsw3tjOxwOPD7/UiShNVqzWq4vhBoMt3y8nJcLhf33XcfiqJQWlrKz372s6wnUefqervzzjvZt2+f3rJsNBo5dOhQJl46R/SlhqqqHDlyRNfUNzQ0cPvtt3PLLbdQVFQETGjAT5w4QVVV1UXZkSWE4NSpU0SjUYxG40XR5ZaIvr4+nE6nftwRQvC5z32OU6dOUVhYSF9fHy+99NKStjNnETmiX0zQZJEPP/wwTz75JNXV1VxzzTU8/fTTfPe7373o+tbhAsktFouukEvscissLNS73JZCXtnf38/w8LCe/RdCcP/999Pd3c0Pf/hDDAYD0Wh00b3xFhE5ol+sEELwzDPP8IEPfICVK1eSn5+va+q1QQFLjVSGHQoh8Hq9OBwO3XRSK9stxu6pNetovfVCCP7t3/6N06dP8+Mf//iNuoMnIutEX/qY7XUKSZI4cOAA+/fv58UXX+Tb3/42Xq+X973vfdx222088MADDA0NJS3bLAY055V4vXYySJJEcXExa9as4bLLLmPVqlUEAgEOHz7M0aNH6e/vJxKJZGWNg4OD00j+zW9+k+PHj/Pggw9mjORPP/0069ato7GxkS9/+cvTfi+E4JOf/CSNjY00NTVx5MiRjLzuxYTcjp5haA6zmqZelmXe9ra3cccdd1BTU7MoSTpN615WVqbbK80HgUBA16lLkqRbamVCnz40NERfXx9bt27FaDQihOC//uu/eP7553nkkUcy1jOfSmvrk08+yTe/+U2efPJJXnvtNe6+++5Mtbamilzo/npGvKb+l7/8JZFIRHfPyfRsNw2ar3llZWVGE4OJTrPxdtjpYnh4mJ6eHrZt26aT/Pvf/z5PPfUUv/zlLzNqdJFKa+tf/MVfcPXVV/P+978fgHXr1vH8888v5hy5XAvs6xmSJFFbW8snP/lJPvGJTzA8PMyjjz7K3Xffjdfr5ZZbbuGOO+6gsbExI6TXhh1qU0YzCavVSn19PfX19frI4rNnzxIKhfRafSr97A6HQ7ez1kLzH//4x+zfv1+3EsskUjV0THxMf3//kgyMzBZyRF8kSJJEdXU1H/vYx/jYxz6Gy+Xiscce495778XlcnHTTTexd+9eXaGVLrT53/X19VkfxBg/slhzbu3u7sbn81FaWkpVVVVSXb3T6Zymd3/ooYf4xS9+weOPP54VX7pUWlvTaX99vSJH9CVCeXk5d955J3feeScej4f9+/fzxS9+kd7eXm688Ube/va3s3nz5pRq3Nq01YaGBiorU5+3ngkkOreOjIxMsZeuqqqipKQEj8ejO9doJN+3bx8/+tGPePzxx7PmMJvqCONU2l9fz7joz+hut5v3vve9dHV10dDQwP/+7/9Om3ja29vLn/3ZnzE0NIQsy3z0ox/l7rvvXqIVLwxer5fHH3+cffv2ce7cOa6//nr27t07o6Y+2bDDiwHxtXqn06knxaqqqjAYDOzfv59vfetbPP744ymPdpoPUmltfeKJJ/jWt76lJ+M++clPcuDAgaytKQlyybhPf/rTlJaWcu+99/LlL38Zj8eju3xo0Mo027dvZ3x8nB07dvDYY49NG5XzeoPP5+Opp55i3759tLa2cs0117B37152796NwWDQrakW6lefTbjdbtra2lizZg0ej4cf/ehHvPLKK7hcLn7zm9+wcuXKrK9hrtZWIQR33XUXTz/9NDabjR/84Afs3Lkz6+uKQ47o8RnQwcFBrr76atra2mb9m71793LXXXdxww03LNIqs49QKMRvfvMbHn74YY4ePcqOHTs4ePAgv/zlLxdUQssmNE/9bdu26WrA3/zmN3z5y1/mmmuu4bnnnuMf/uEfuPXWW5d4pUuOHNHtdjujo6P6v7Xz3kzo6uriqquu0id4vBFx+vRpbrvtNrZu3cqZM2e44ooruOOOO3jzm9980bSJasMf4n3hf//73/P5z3+eJ554gqqqKgB90u4ljkujvHb99dczNDQ07ef33XdfWs/j8/l45zvfyde//vU3LMkBTp06xcMPP8z27duJRqO88MILPPLII3zmM59h586dC9bULxRjY2PTSP7SSy/x93//9zz++OM6yeGNl92+WHHR7+iphu7RaJTbbruNt771rXzqU59agpUuPWKx2BRNfVNTE3v37k1LU79QaG63W7du1V/ztdde41Of+hT79++fUq/OFN4ACdtc6P53f/d3lJWV6ck4t9vNV7/61SmPEULwgQ98gNLSUr7+9a8vzUIvMiiKwquvvsq+fft45plnWLduHXfccQc33nhj1kpZ2tRVzTQC4MiRI3z84x/nV7/6FQ0NDVl53TdAwjb7YY0QYrb/lhwul0tce+21orGxUVx77bViZGRECCFEf3+/uPnmm4UQQvzhD38QgNiyZYtobm4Wzc3N4oknnljKZV9UUBRFHDhwQHz6058Wzc3N4o477hDf//73xeDgoPD7/Rn5b3h4WDzzzDPC4XDoP3v55ZfFli1bxNmzZ7P6/tauXSsGBgaEEEIMDAyItWvXzvk3t99+u/jNb36T1XWlgbl4uOD/LvodPYfMQlO1Pfzwwzz11FNUV1frc+oTw91U4fP5aGlpmTJaubW1lQ9/+MM8/PDDrFu3LpNvYRreAAnbXOieQ/YgJk0pHnnkER5//HFKS0unzKlPBX6/nxMnTrBlyxbdZuvMmTN88IMf5Oc///mMk0bTxWwJ2w984AMpE93n8/GWt7yFz33uc7zjHe/IyNoygFzovph46qmnxNq1a8Xq1avF/fffP+33qqqKT3ziE2L16tViy5Yt4vDhw0uwyuxAVVXR1tYm7rvvPnHZZZeJa665Rnzta18THR0dwufzJQ3XnU6neOaZZ8TQ0JD+s2PHjoktW7aIY8eOLdraUw3dI5GIuPHGG8W//du/LdraUkTWQ/cc0ScRi8XEqlWrREdHhwiHw6KpqUm0trZOecwTTzwhbrrpJqGqqnjllVfE7t27l2i12YWqqqKjo0N89atfFXv27BFvfvObxVe/+lXR3t6uk97hcEwjeWtrq2hqahKHDh1a1PX+7d/+rX5jvv/++8Xf/d3fJX1Pf/qnfyruvvvuRV1bisgRfbHw8ssvixtvvFH/95e+9CXxpS99acpjPvrRj4qf/exn+r/jd5I3KlRVFb29veLrX/+6uOqqq8QVV1whPvvZz4rdu3eL3t5eneRnzpwRzc3N4tVXX130Nb4BErZZJ/pF0TBzMSCnW04OSZKoq6vj7rvv5pOf/CRHjx7VNfTvfOc7ufXWW7niiiv49Kc/zbe+9S0uu+yyRV9jWVkZzz777LSf19TU8OSTTwJw5ZVXTuxslyhyRJ9EsovgUtQtzwZJknjppZf4xS9+wRVXXIHT6eSxxx7jYx/7GP/8z//MlVdeudRLzGEG5Ig+iZxuOTV84hOf0P9/RUUFH/nIR/jIRz6yhCvKIRXkXGAnsWvXLs6ePUtnZyeRSISHHnqI22+/fcpjbr/9dh588EGEELz66qsUFxe/ocP2pYbb7eaGG25gzZo13HDDDbPWxhVFYdu2bdx2222LuMLXD3JEn4TRaORb3/oWb33rW9mwYQPvec972LRpE9/97nd17fItt9zCqlWraGxs5CMf+Qjf+c53lnjVb2x8+ctf5rrrruPs2bNcd911Sa2aNXzjG99gw4YNi7i61xnmyNblkMOSIdX6eG9vr7j22mvFs88+K2699dbFXGKmkPWse25Hz+GixfDwsH40WrZsGQ6HI+nj7rnnHr761a9eFDPkLlbkPpmLAHNNEvnpT39KU1MTTU1N7Nmzh+PHjy/BKrOD66+/ns2bN0/771e/+lVKf//4449TWVnJjh07srzS1znm2PJzyDJS6ch76aWXhNvtFkII8eSTT75hO/ISkUrofu+994ra2lqxYsUKUVVVJfLy8sQf//EfL/ZSF4pc6P5Gx4EDB2hsbGTVqlWYzWbe9773TdvN9uzZoyvLLr/8cvr6+pZiqYuO22+/nR/96EcA/OhHP2Lv3r3THnP//ffT19dHV1cXDz30ENdeey0/+clPFnupFz1yRF9izNRtNxO+973vcfPNNy/G0pYc9957L7/97W9Zs2YNv/3tb7n33nuBiQmst9xyyxKv7vWFXMPMEkOk0W333HPP8b3vfY8XX3wx28u6KJBKa2s8rr76aq6++upFWNnrDzmiLzFS7bY7ceIEd955J0899RRlZWWLucQc3gDIhe5LjFQ68np6enjHO97Bj3/8Y9auXbtEK83h9Yzcjr7EiO/I0yaJaB15MDFJ5Itf/CIjIyP81V/9lf43hw4dWspl5/A6w1xWUjnkkMMbALnQPYccLgHkiH6JQ5KkmyRJapMk6ZwkSffO8rhdkiQpkiS9azHXl0NmkCP6JQxJkgzAt4GbgY3A+yVJmjbRYPJxXwF+vbgrzCFTyBH90sZu4JwQ4rwQIgI8BExvP4NPAPuA5KqSHC565Ih+aaMW6I37d9/kz3RIklQLvB347iKuK4cMI0f0SxvJWvASyzBfBz4jhFCyv5wcsoVcHf3SRh8QP960DhhIeMxO4KHJttxy4BZJkmJCiMcWZYU5ZAS5OvolDEmSjEA7cB3QDxwE/kgI0TrD438IPC6EeGTRFplDRpDb0S9hCCFikiTdxUQ23QB8XwjRKknSX07+Pncuf4Mgt6PnkMMlgFwyLoccLgHkiJ5DDpcAckTPIYdLADmi55DDJYAc0XPI4RJAjug55HAJIEf0HHK4BJAjeg45XAL4/wGdRS1pdo8oOwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制X2，此时，X2的所有样本点分布在一个平面上\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X2[:,0], X2[:,1], X2[:,2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.44401532, -0.03133187,  0.89547122])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w2 = first_component(X2, initial_w, eta)\n",
    "w2 # 求出第二主成分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 将X2去除在第二主成分上的分量，得到X3\n",
    "X3 = np.empty(X2.shape)\n",
    "for i in range(len(X)):\n",
    "    X3[i] = X2[i] - X2[i].dot(w2) * w2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制X3，此时，X3的所有样本点分布在一条直线上\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X3[:,0], X3[:,1], X3[:,2])\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
